diff --git a/gtsam/hybrid/HybridBayesTree.cpp b/gtsam/hybrid/HybridBayesTree.cpp
index 400cac5e7..ff07f1817 100644
--- a/gtsam/hybrid/HybridBayesTree.cpp
+++ b/gtsam/hybrid/HybridBayesTree.cpp
@@ -11,7 +11,8 @@
 
 /**
  * @file    HybridBayesTree.cpp
- * @brief   Hybrid Bayes Tree, the result of eliminating a HybridJunctionTree
+ * @brief   Hybrid Bayes Tree, the result of eliminating a
+ * HybridGaussianJunctionTree
  * @date Mar 11, 2022
  * @author  Fan Jiang
  */
@@ -26,7 +27,7 @@ namespace gtsam {
 
 // Instantiate base class
 template class BayesTreeCliqueBase<HybridBayesTreeClique,
-                                   GaussianHybridFactorGraph>;
+                                   HybridGaussianFactorGraph>;
 template class BayesTree<HybridBayesTreeClique>;
 
 /* ************************************************************************* */
diff --git a/gtsam/hybrid/HybridBayesTree.h b/gtsam/hybrid/HybridBayesTree.h
index 610181458..28d9ef809 100644
--- a/gtsam/hybrid/HybridBayesTree.h
+++ b/gtsam/hybrid/HybridBayesTree.h
@@ -11,15 +11,16 @@
 
 /**
  * @file    HybridBayesTree.h
- * @brief   Hybrid Bayes Tree, the result of eliminating a HybridJunctionTree
+ * @brief   Hybrid Bayes Tree, the result of eliminating a
+ * HybridGaussianJunctionTree
  * @date Mar 11, 2022
  * @author  Fan Jiang
  */
 
 #pragma once
 
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/HybridBayesNet.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/inference/BayesTree.h>
 #include <gtsam/inference/BayesTreeCliqueBase.h>
 #include <gtsam/inference/Conditional.h>
@@ -38,10 +39,10 @@ class VectorValues;
  */
 class GTSAM_EXPORT HybridBayesTreeClique
     : public BayesTreeCliqueBase<HybridBayesTreeClique,
-                                 GaussianHybridFactorGraph> {
+                                 HybridGaussianFactorGraph> {
  public:
   typedef HybridBayesTreeClique This;
-  typedef BayesTreeCliqueBase<HybridBayesTreeClique, GaussianHybridFactorGraph>
+  typedef BayesTreeCliqueBase<HybridBayesTreeClique, HybridGaussianFactorGraph>
       Base;
   typedef boost::shared_ptr<This> shared_ptr;
   typedef boost::weak_ptr<This> weak_ptr;
diff --git a/gtsam/hybrid/HybridConditional.h b/gtsam/hybrid/HybridConditional.h
index 9592b0c69..887b49f12 100644
--- a/gtsam/hybrid/HybridConditional.h
+++ b/gtsam/hybrid/HybridConditional.h
@@ -18,9 +18,9 @@
 #pragma once
 
 #include <gtsam/discrete/DiscreteConditional.h>
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/GaussianMixtureConditional.h>
 #include <gtsam/hybrid/HybridFactor.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/inference/Conditional.h>
 #include <gtsam/inference/Key.h>
 #include <gtsam/linear/GaussianConditional.h>
@@ -34,7 +34,7 @@
 
 namespace gtsam {
 
-class GaussianHybridFactorGraph;
+class HybridGaussianFactorGraph;
 
 /**
  * Hybrid Conditional Density
diff --git a/gtsam/hybrid/HybridEliminationTree.cpp b/gtsam/hybrid/HybridEliminationTree.cpp
index 148685327..c2df2dd60 100644
--- a/gtsam/hybrid/HybridEliminationTree.cpp
+++ b/gtsam/hybrid/HybridEliminationTree.cpp
@@ -21,17 +21,17 @@
 namespace gtsam {
 
 // Instantiate base class
-template class EliminationTree<HybridBayesNet, GaussianHybridFactorGraph>;
+template class EliminationTree<HybridBayesNet, HybridGaussianFactorGraph>;
 
 /* ************************************************************************* */
 HybridEliminationTree::HybridEliminationTree(
-    const GaussianHybridFactorGraph& factorGraph,
+    const HybridGaussianFactorGraph& factorGraph,
     const VariableIndex& structure, const Ordering& order)
     : Base(factorGraph, structure, order) {}
 
 /* ************************************************************************* */
 HybridEliminationTree::HybridEliminationTree(
-    const GaussianHybridFactorGraph& factorGraph, const Ordering& order)
+    const HybridGaussianFactorGraph& factorGraph, const Ordering& order)
     : Base(factorGraph, order) {}
 
 /* ************************************************************************* */
diff --git a/gtsam/hybrid/HybridEliminationTree.h b/gtsam/hybrid/HybridEliminationTree.h
index 04bd9cd35..77a84fea8 100644
--- a/gtsam/hybrid/HybridEliminationTree.h
+++ b/gtsam/hybrid/HybridEliminationTree.h
@@ -17,8 +17,8 @@
 
 #pragma once
 
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/HybridBayesNet.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/inference/EliminationTree.h>
 
 namespace gtsam {
@@ -27,12 +27,12 @@ namespace gtsam {
  * Elimination Tree type for Hybrid
  */
 class GTSAM_EXPORT HybridEliminationTree
-    : public EliminationTree<HybridBayesNet, GaussianHybridFactorGraph> {
+    : public EliminationTree<HybridBayesNet, HybridGaussianFactorGraph> {
  private:
   friend class ::EliminationTreeTester;
 
  public:
-  typedef EliminationTree<HybridBayesNet, GaussianHybridFactorGraph>
+  typedef EliminationTree<HybridBayesNet, HybridGaussianFactorGraph>
       Base;                                    ///< Base class
   typedef HybridEliminationTree This;          ///< This class
   typedef boost::shared_ptr<This> shared_ptr;  ///< Shared pointer to this class
@@ -49,7 +49,7 @@ class GTSAM_EXPORT HybridEliminationTree
    * named constructor instead.
    * @return The elimination tree
    */
-  HybridEliminationTree(const GaussianHybridFactorGraph& factorGraph,
+  HybridEliminationTree(const HybridGaussianFactorGraph& factorGraph,
                         const VariableIndex& structure, const Ordering& order);
 
   /** Build the elimination tree of a factor graph.  Note that this has to
@@ -57,7 +57,7 @@ class GTSAM_EXPORT HybridEliminationTree
    * this precomputed, use the other constructor instead.
    * @param factorGraph The factor graph for which to build the elimination tree
    */
-  HybridEliminationTree(const GaussianHybridFactorGraph& factorGraph,
+  HybridEliminationTree(const HybridGaussianFactorGraph& factorGraph,
                         const Ordering& order);
 
   /// @}
diff --git a/gtsam/hybrid/GaussianHybridFactorGraph.cpp b/gtsam/hybrid/HybridGaussianFactorGraph.cpp
similarity index 94%
rename from gtsam/hybrid/GaussianHybridFactorGraph.cpp
rename to gtsam/hybrid/HybridGaussianFactorGraph.cpp
index 3354d5b4d..0ac2c2656 100644
--- a/gtsam/hybrid/GaussianHybridFactorGraph.cpp
+++ b/gtsam/hybrid/HybridGaussianFactorGraph.cpp
@@ -10,7 +10,7 @@
  * -------------------------------------------------------------------------- */
 
 /**
- * @file   GaussianHybridFactorGraph.cpp
+ * @file   HybridGaussianFactorGraph.cpp
  * @brief  Hybrid factor graph that uses type erasure
  * @author Fan Jiang
  * @author Varun Agrawal
@@ -23,7 +23,6 @@
 #include <gtsam/discrete/DiscreteEliminationTree.h>
 #include <gtsam/discrete/DiscreteFactorGraph.h>
 #include <gtsam/discrete/DiscreteJunctionTree.h>
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/GaussianMixtureConditional.h>
 #include <gtsam/hybrid/GaussianMixtureFactor.h>
 #include <gtsam/hybrid/HybridConditional.h>
@@ -31,7 +30,8 @@
 #include <gtsam/hybrid/HybridEliminationTree.h>
 #include <gtsam/hybrid/HybridFactor.h>
 #include <gtsam/hybrid/HybridGaussianFactor.h>
-#include <gtsam/hybrid/HybridJunctionTree.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+#include <gtsam/hybrid/HybridGaussianJunctionTree.h>
 #include <gtsam/inference/EliminateableFactorGraph-inst.h>
 #include <gtsam/inference/Key.h>
 #include <gtsam/linear/GaussianConditional.h>
@@ -53,7 +53,7 @@
 
 namespace gtsam {
 
-template class EliminateableFactorGraph<GaussianHybridFactorGraph>;
+template class EliminateableFactorGraph<HybridGaussianFactorGraph>;
 
 /* ************************************************************************ */
 static GaussianMixtureFactor::Sum &addGaussian(
@@ -78,7 +78,7 @@ static GaussianMixtureFactor::Sum &addGaussian(
 
 /* ************************************************************************ */
 std::pair<HybridConditional::shared_ptr, HybridFactor::shared_ptr>
-continuousElimination(const GaussianHybridFactorGraph &factors,
+continuousElimination(const HybridGaussianFactorGraph &factors,
                       const Ordering &frontalKeys) {
   GaussianFactorGraph gfg;
   for (auto &fp : factors) {
@@ -103,7 +103,7 @@ continuousElimination(const GaussianHybridFactorGraph &factors,
 
 /* ************************************************************************ */
 std::pair<HybridConditional::shared_ptr, HybridFactor::shared_ptr>
-discreteElimination(const GaussianHybridFactorGraph &factors,
+discreteElimination(const HybridGaussianFactorGraph &factors,
                     const Ordering &frontalKeys) {
   DiscreteFactorGraph dfg;
   for (auto &fp : factors) {
@@ -129,7 +129,7 @@ discreteElimination(const GaussianHybridFactorGraph &factors,
 
 /* ************************************************************************ */
 std::pair<HybridConditional::shared_ptr, HybridFactor::shared_ptr>
-hybridElimination(const GaussianHybridFactorGraph &factors,
+hybridElimination(const HybridGaussianFactorGraph &factors,
                   const Ordering &frontalKeys,
                   const KeySet &continuousSeparator,
                   const std::set<DiscreteKey> &discreteSeparatorSet) {
@@ -236,7 +236,7 @@ hybridElimination(const GaussianHybridFactorGraph &factors,
 }
 /* ************************************************************************ */
 std::pair<HybridConditional::shared_ptr, HybridFactor::shared_ptr>  //
-EliminateHybrid(const GaussianHybridFactorGraph &factors,
+EliminateHybrid(const HybridGaussianFactorGraph &factors,
                 const Ordering &frontalKeys) {
   // NOTE: Because we are in the Conditional Gaussian regime there are only
   // a few cases:
@@ -345,22 +345,22 @@ EliminateHybrid(const GaussianHybridFactorGraph &factors,
 }
 
 /* ************************************************************************ */
-void GaussianHybridFactorGraph::add(JacobianFactor &&factor) {
+void HybridGaussianFactorGraph::add(JacobianFactor &&factor) {
   FactorGraph::add(boost::make_shared<HybridGaussianFactor>(std::move(factor)));
 }
 
 /* ************************************************************************ */
-void GaussianHybridFactorGraph::add(JacobianFactor::shared_ptr factor) {
+void HybridGaussianFactorGraph::add(JacobianFactor::shared_ptr factor) {
   FactorGraph::add(boost::make_shared<HybridGaussianFactor>(factor));
 }
 
 /* ************************************************************************ */
-void GaussianHybridFactorGraph::add(DecisionTreeFactor &&factor) {
+void HybridGaussianFactorGraph::add(DecisionTreeFactor &&factor) {
   FactorGraph::add(boost::make_shared<HybridDiscreteFactor>(std::move(factor)));
 }
 
 /* ************************************************************************ */
-void GaussianHybridFactorGraph::add(DecisionTreeFactor::shared_ptr factor) {
+void HybridGaussianFactorGraph::add(DecisionTreeFactor::shared_ptr factor) {
   FactorGraph::add(boost::make_shared<HybridDiscreteFactor>(factor));
 }
 
diff --git a/gtsam/hybrid/GaussianHybridFactorGraph.h b/gtsam/hybrid/HybridGaussianFactorGraph.h
similarity index 77%
rename from gtsam/hybrid/GaussianHybridFactorGraph.h
rename to gtsam/hybrid/HybridGaussianFactorGraph.h
index c8e0718fc..6944af510 100644
--- a/gtsam/hybrid/GaussianHybridFactorGraph.h
+++ b/gtsam/hybrid/HybridGaussianFactorGraph.h
@@ -10,7 +10,7 @@
  * -------------------------------------------------------------------------- */
 
 /**
- * @file   GaussianHybridFactorGraph.h
+ * @file   HybridGaussianFactorGraph.h
  * @brief  Linearized Hybrid factor graph that uses type erasure
  * @author Fan Jiang
  * @date   Mar 11, 2022
@@ -26,36 +26,37 @@
 namespace gtsam {
 
 // Forward declarations
-class GaussianHybridFactorGraph;
+class HybridGaussianFactorGraph;
 class HybridConditional;
 class HybridBayesNet;
 class HybridEliminationTree;
 class HybridBayesTree;
-class HybridJunctionTree;
+class HybridGaussianJunctionTree;
 class DecisionTreeFactor;
 
 class JacobianFactor;
 
-/** Main elimination function for GaussianHybridFactorGraph */
+/** Main elimination function for HybridGaussianFactorGraph */
 GTSAM_EXPORT
 std::pair<boost::shared_ptr<HybridConditional>, HybridFactor::shared_ptr>
-EliminateHybrid(const GaussianHybridFactorGraph& factors, const Ordering& keys);
+EliminateHybrid(const HybridGaussianFactorGraph& factors, const Ordering& keys);
 
 /* ************************************************************************* */
 template <>
-struct EliminationTraits<GaussianHybridFactorGraph> {
+struct EliminationTraits<HybridGaussianFactorGraph> {
   typedef HybridFactor FactorType;  ///< Type of factors in factor graph
-  typedef GaussianHybridFactorGraph
+  typedef HybridGaussianFactorGraph
       FactorGraphType;  ///< Type of the factor graph (e.g.
-                        ///< GaussianHybridFactorGraph)
+                        ///< HybridGaussianFactorGraph)
   typedef HybridConditional
       ConditionalType;  ///< Type of conditionals from elimination
   typedef HybridBayesNet
       BayesNetType;  ///< Type of Bayes net from sequential elimination
   typedef HybridEliminationTree
-      EliminationTreeType;                      ///< Type of elimination tree
-  typedef HybridBayesTree BayesTreeType;        ///< Type of Bayes tree
-  typedef HybridJunctionTree JunctionTreeType;  ///< Type of Junction tree
+      EliminationTreeType;                ///< Type of elimination tree
+  typedef HybridBayesTree BayesTreeType;  ///< Type of Bayes tree
+  typedef HybridGaussianJunctionTree
+      JunctionTreeType;  ///< Type of Junction tree
   /// The default dense elimination function
   static std::pair<boost::shared_ptr<ConditionalType>,
                    boost::shared_ptr<FactorType> >
@@ -70,12 +71,12 @@ struct EliminationTraits<GaussianHybridFactorGraph> {
  * This is the linearized version of a hybrid factor graph.
  * Everything inside needs to be hybrid factor or hybrid conditional.
  */
-class GaussianHybridFactorGraph
+class HybridGaussianFactorGraph
     : public FactorGraph<HybridFactor>,
-      public EliminateableFactorGraph<GaussianHybridFactorGraph> {
+      public EliminateableFactorGraph<HybridGaussianFactorGraph> {
  public:
   using Base = FactorGraph<HybridFactor>;
-  using This = GaussianHybridFactorGraph;  ///< this class
+  using This = HybridGaussianFactorGraph;  ///< this class
   using BaseEliminateable =
       EliminateableFactorGraph<This>;          ///< for elimination
   using shared_ptr = boost::shared_ptr<This>;  ///< shared_ptr to This
@@ -86,7 +87,7 @@ class GaussianHybridFactorGraph
   /// @name Constructors
   /// @{
 
-  GaussianHybridFactorGraph() = default;
+  HybridGaussianFactorGraph() = default;
 
   /**
    * Implicit copy/downcast constructor to override explicit template container
@@ -94,7 +95,7 @@ class GaussianHybridFactorGraph
    * `cachedSeparatorMarginal_.reset(*separatorMarginal)`
    * */
   template <class DERIVEDFACTOR>
-  GaussianHybridFactorGraph(const FactorGraph<DERIVEDFACTOR>& graph)
+  HybridGaussianFactorGraph(const FactorGraph<DERIVEDFACTOR>& graph)
       : Base(graph) {}
 
   /// @}
diff --git a/gtsam/hybrid/HybridISAM.cpp b/gtsam/hybrid/HybridGaussianISAM.cpp
similarity index 84%
rename from gtsam/hybrid/HybridISAM.cpp
rename to gtsam/hybrid/HybridGaussianISAM.cpp
index 476149126..7783a88dd 100644
--- a/gtsam/hybrid/HybridISAM.cpp
+++ b/gtsam/hybrid/HybridGaussianISAM.cpp
@@ -10,16 +10,16 @@
  * -------------------------------------------------------------------------- */
 
 /**
- * @file HybridISAM.h
+ * @file HybridGaussianISAM.h
  * @date March 31, 2022
  * @author Fan Jiang
  * @author Frank Dellaert
  * @author Richard Roberts
  */
 
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/HybridBayesTree.h>
-#include <gtsam/hybrid/HybridISAM.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+#include <gtsam/hybrid/HybridGaussianISAM.h>
 #include <gtsam/inference/ISAM-inst.h>
 #include <gtsam/inference/Key.h>
 
@@ -31,15 +31,17 @@ namespace gtsam {
 // template class ISAM<HybridBayesTree>;
 
 /* ************************************************************************* */
-HybridISAM::HybridISAM() {}
+HybridGaussianISAM::HybridGaussianISAM() {}
 
 /* ************************************************************************* */
-HybridISAM::HybridISAM(const HybridBayesTree& bayesTree) : Base(bayesTree) {}
+HybridGaussianISAM::HybridGaussianISAM(const HybridBayesTree& bayesTree)
+    : Base(bayesTree) {}
 
 /* ************************************************************************* */
-void HybridISAM::updateInternal(const GaussianHybridFactorGraph& newFactors,
-                                HybridBayesTree::Cliques* orphans,
-                                const HybridBayesTree::Eliminate& function) {
+void HybridGaussianISAM::updateInternal(
+    const HybridGaussianFactorGraph& newFactors,
+    HybridBayesTree::Cliques* orphans,
+    const HybridBayesTree::Eliminate& function) {
   // Remove the contaminated part of the Bayes tree
   BayesNetType bn;
   const KeySet newFactorKeys = newFactors.keys();
@@ -90,8 +92,8 @@ void HybridISAM::updateInternal(const GaussianHybridFactorGraph& newFactors,
 }
 
 /* ************************************************************************* */
-void HybridISAM::update(const GaussianHybridFactorGraph& newFactors,
-                        const HybridBayesTree::Eliminate& function) {
+void HybridGaussianISAM::update(const HybridGaussianFactorGraph& newFactors,
+                                const HybridBayesTree::Eliminate& function) {
   Cliques orphans;
   this->updateInternal(newFactors, &orphans, function);
 }
diff --git a/gtsam/hybrid/HybridISAM.h b/gtsam/hybrid/HybridGaussianISAM.h
similarity index 76%
rename from gtsam/hybrid/HybridISAM.h
rename to gtsam/hybrid/HybridGaussianISAM.h
index fae7efafd..d5b6271da 100644
--- a/gtsam/hybrid/HybridISAM.h
+++ b/gtsam/hybrid/HybridGaussianISAM.h
@@ -10,7 +10,7 @@
  * -------------------------------------------------------------------------- */
 
 /**
- * @file HybridISAM.h
+ * @file HybridGaussianISAM.h
  * @date March 31, 2022
  * @author Fan Jiang
  * @author Frank Dellaert
@@ -20,33 +20,33 @@
 #pragma once
 
 #include <gtsam/base/Testable.h>
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/HybridBayesTree.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/inference/ISAM.h>
 
 namespace gtsam {
 
-class GTSAM_EXPORT HybridISAM : public ISAM<HybridBayesTree> {
+class GTSAM_EXPORT HybridGaussianISAM : public ISAM<HybridBayesTree> {
  public:
   typedef ISAM<HybridBayesTree> Base;
-  typedef HybridISAM This;
+  typedef HybridGaussianISAM This;
   typedef boost::shared_ptr<This> shared_ptr;
 
   /// @name Standard Constructors
   /// @{
 
   /** Create an empty Bayes Tree */
-  HybridISAM();
+  HybridGaussianISAM();
 
   /** Copy constructor */
-  HybridISAM(const HybridBayesTree& bayesTree);
+  HybridGaussianISAM(const HybridBayesTree& bayesTree);
 
   /// @}
 
  private:
   /// Internal method that performs the ISAM update.
   void updateInternal(
-      const GaussianHybridFactorGraph& newFactors,
+      const HybridGaussianFactorGraph& newFactors,
       HybridBayesTree::Cliques* orphans,
       const HybridBayesTree::Eliminate& function =
           HybridBayesTree::EliminationTraitsType::DefaultEliminate);
@@ -58,13 +58,13 @@ class GTSAM_EXPORT HybridISAM : public ISAM<HybridBayesTree> {
    * @param newFactors Factor graph of new factors to add and eliminate.
    * @param function Elimination function.
    */
-  void update(const GaussianHybridFactorGraph& newFactors,
+  void update(const HybridGaussianFactorGraph& newFactors,
               const HybridBayesTree::Eliminate& function =
                   HybridBayesTree::EliminationTraitsType::DefaultEliminate);
 };
 
 /// traits
 template <>
-struct traits<HybridISAM> : public Testable<HybridISAM> {};
+struct traits<HybridGaussianISAM> : public Testable<HybridGaussianISAM> {};
 
 }  // namespace gtsam
diff --git a/gtsam/hybrid/HybridJunctionTree.cpp b/gtsam/hybrid/HybridGaussianJunctionTree.cpp
similarity index 73%
rename from gtsam/hybrid/HybridJunctionTree.cpp
rename to gtsam/hybrid/HybridGaussianJunctionTree.cpp
index 8fa3aa033..8ceb7c87b 100644
--- a/gtsam/hybrid/HybridJunctionTree.cpp
+++ b/gtsam/hybrid/HybridGaussianJunctionTree.cpp
@@ -10,14 +10,14 @@
  * -------------------------------------------------------------------------- */
 
 /**
- * @file HybridJunctionTree.cpp
+ * @file HybridGaussianJunctionTree.cpp
  * @date Mar 11, 2022
  * @author Fan Jiang
  */
 
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/HybridEliminationTree.h>
-#include <gtsam/hybrid/HybridJunctionTree.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+#include <gtsam/hybrid/HybridGaussianJunctionTree.h>
 #include <gtsam/inference/JunctionTree-inst.h>
 #include <gtsam/inference/Key.h>
 
@@ -27,19 +27,19 @@ namespace gtsam {
 
 // Instantiate base classes
 template class EliminatableClusterTree<HybridBayesTree,
-                                       GaussianHybridFactorGraph>;
-template class JunctionTree<HybridBayesTree, GaussianHybridFactorGraph>;
+                                       HybridGaussianFactorGraph>;
+template class JunctionTree<HybridBayesTree, HybridGaussianFactorGraph>;
 
 struct HybridConstructorTraversalData {
   typedef
-      typename JunctionTree<HybridBayesTree, GaussianHybridFactorGraph>::Node
+      typename JunctionTree<HybridBayesTree, HybridGaussianFactorGraph>::Node
           Node;
   typedef
       typename JunctionTree<HybridBayesTree,
-                            GaussianHybridFactorGraph>::sharedNode sharedNode;
+                            HybridGaussianFactorGraph>::sharedNode sharedNode;
 
   HybridConstructorTraversalData* const parentData;
-  sharedNode myJTNode;
+  sharedNode junctionTreeNode;
   FastVector<SymbolicConditional::shared_ptr> childSymbolicConditionals;
   FastVector<SymbolicFactor::shared_ptr> childSymbolicFactors;
   KeySet discreteKeys;
@@ -57,24 +57,24 @@ struct HybridConstructorTraversalData {
     // On the pre-order pass, before children have been visited, we just set up
     // a traversal data structure with its own JT node, and create a child
     // pointer in its parent.
-    HybridConstructorTraversalData myData =
+    HybridConstructorTraversalData data =
         HybridConstructorTraversalData(&parentData);
-    myData.myJTNode = boost::make_shared<Node>(node->key, node->factors);
-    parentData.myJTNode->addChild(myData.myJTNode);
+    data.junctionTreeNode = boost::make_shared<Node>(node->key, node->factors);
+    parentData.junctionTreeNode->addChild(data.junctionTreeNode);
 
     for (HybridFactor::shared_ptr& f : node->factors) {
       for (auto& k : f->discreteKeys()) {
-        myData.discreteKeys.insert(k.first);
+        data.discreteKeys.insert(k.first);
       }
     }
 
-    return myData;
+    return data;
   }
 
   // Post-order visitor function
   static void ConstructorTraversalVisitorPostAlg2(
       const boost::shared_ptr<HybridEliminationTree::Node>& ETreeNode,
-      const HybridConstructorTraversalData& myData) {
+      const HybridConstructorTraversalData& data) {
     // In this post-order visitor, we combine the symbolic elimination results
     // from the elimination tree children and symbolically eliminate the current
     // elimination tree node.  We then check whether each of our elimination
@@ -87,50 +87,50 @@ struct HybridConstructorTraversalData {
     // Do symbolic elimination for this node
     SymbolicFactors symbolicFactors;
     symbolicFactors.reserve(ETreeNode->factors.size() +
-                            myData.childSymbolicFactors.size());
+                            data.childSymbolicFactors.size());
     // Add ETree node factors
     symbolicFactors += ETreeNode->factors;
     // Add symbolic factors passed up from children
-    symbolicFactors += myData.childSymbolicFactors;
+    symbolicFactors += data.childSymbolicFactors;
 
     Ordering keyAsOrdering;
     keyAsOrdering.push_back(ETreeNode->key);
-    SymbolicConditional::shared_ptr myConditional;
-    SymbolicFactor::shared_ptr mySeparatorFactor;
-    boost::tie(myConditional, mySeparatorFactor) =
+    SymbolicConditional::shared_ptr conditional;
+    SymbolicFactor::shared_ptr separatorFactor;
+    boost::tie(conditional, separatorFactor) =
         internal::EliminateSymbolic(symbolicFactors, keyAsOrdering);
 
     // Store symbolic elimination results in the parent
-    myData.parentData->childSymbolicConditionals.push_back(myConditional);
-    myData.parentData->childSymbolicFactors.push_back(mySeparatorFactor);
-    myData.parentData->discreteKeys.merge(myData.discreteKeys);
+    data.parentData->childSymbolicConditionals.push_back(conditional);
+    data.parentData->childSymbolicFactors.push_back(separatorFactor);
+    data.parentData->discreteKeys.merge(data.discreteKeys);
 
-    sharedNode node = myData.myJTNode;
+    sharedNode node = data.junctionTreeNode;
     const FastVector<SymbolicConditional::shared_ptr>& childConditionals =
-        myData.childSymbolicConditionals;
-    node->problemSize_ = (int)(myConditional->size() * symbolicFactors.size());
+        data.childSymbolicConditionals;
+    node->problemSize_ = (int)(conditional->size() * symbolicFactors.size());
 
     // Merge our children if they are in our clique - if our conditional has
     // exactly one fewer parent than our child's conditional.
-    const size_t myNrParents = myConditional->nrParents();
+    const size_t nrParents = conditional->nrParents();
     const size_t nrChildren = node->nrChildren();
     assert(childConditionals.size() == nrChildren);
 
     // decide which children to merge, as index into children
-    std::vector<size_t> nrFrontals = node->nrFrontalsOfChildren();
+    std::vector<size_t> nrChildrenFrontals = node->nrFrontalsOfChildren();
     std::vector<bool> merge(nrChildren, false);
-    size_t myNrFrontals = 1;
+    size_t nrFrontals = 1;
     for (size_t i = 0; i < nrChildren; i++) {
       // Check if we should merge the i^th child
-      if (myNrParents + myNrFrontals == childConditionals[i]->nrParents()) {
+      if (nrParents + nrFrontals == childConditionals[i]->nrParents()) {
         const bool myType =
-            myData.discreteKeys.exists(myConditional->frontals()[0]);
+            data.discreteKeys.exists(conditional->frontals()[0]);
         const bool theirType =
-            myData.discreteKeys.exists(childConditionals[i]->frontals()[0]);
+            data.discreteKeys.exists(childConditionals[i]->frontals()[0]);
 
         if (myType == theirType) {
           // Increment number of frontal variables
-          myNrFrontals += nrFrontals[i];
+          nrFrontals += nrChildrenFrontals[i];
           merge[i] = true;
         }
       }
@@ -142,7 +142,7 @@ struct HybridConstructorTraversalData {
 };
 
 /* ************************************************************************* */
-HybridJunctionTree::HybridJunctionTree(
+HybridGaussianJunctionTree::HybridGaussianJunctionTree(
     const HybridEliminationTree& eliminationTree) {
   gttic(JunctionTree_FromEliminationTree);
   // Here we rely on the BayesNet having been produced by this elimination tree,
@@ -156,7 +156,7 @@ HybridJunctionTree::HybridJunctionTree(
   // as we go.  Gather the created junction tree roots in a dummy Node.
   typedef HybridConstructorTraversalData Data;
   Data rootData(0);
-  rootData.myJTNode =
+  rootData.junctionTreeNode =
       boost::make_shared<typename Base::Node>();  // Make a dummy node to gather
                                                   // the junction tree roots
   treeTraversal::DepthFirstForest(eliminationTree, rootData,
@@ -164,7 +164,7 @@ HybridJunctionTree::HybridJunctionTree(
                                   Data::ConstructorTraversalVisitorPostAlg2);
 
   // Assign roots from the dummy node
-  this->addChildrenAsRoots(rootData.myJTNode);
+  this->addChildrenAsRoots(rootData.junctionTreeNode);
 
   // Transfer remaining factors from elimination tree
   Base::remainingFactors_ = eliminationTree.remainingFactors();
diff --git a/gtsam/hybrid/HybridJunctionTree.h b/gtsam/hybrid/HybridGaussianJunctionTree.h
similarity index 84%
rename from gtsam/hybrid/HybridJunctionTree.h
rename to gtsam/hybrid/HybridGaussianJunctionTree.h
index ce9b818e6..314e7daa6 100644
--- a/gtsam/hybrid/HybridJunctionTree.h
+++ b/gtsam/hybrid/HybridGaussianJunctionTree.h
@@ -10,15 +10,15 @@
  * -------------------------------------------------------------------------- */
 
 /**
- * @file HybridJunctionTree.h
+ * @file HybridGaussianJunctionTree.h
  * @date Mar 11, 2022
  * @author Fan Jiang
  */
 
 #pragma once
 
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/HybridBayesTree.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/inference/JunctionTree.h>
 
 namespace gtsam {
@@ -48,12 +48,12 @@ class HybridEliminationTree;
  * \addtogroup Multifrontal
  * \nosubgrouping
  */
-class GTSAM_EXPORT HybridJunctionTree
-    : public JunctionTree<HybridBayesTree, GaussianHybridFactorGraph> {
+class GTSAM_EXPORT HybridGaussianJunctionTree
+    : public JunctionTree<HybridBayesTree, HybridGaussianFactorGraph> {
  public:
-  typedef JunctionTree<HybridBayesTree, GaussianHybridFactorGraph>
+  typedef JunctionTree<HybridBayesTree, HybridGaussianFactorGraph>
       Base;                                    ///< Base class
-  typedef HybridJunctionTree This;             ///< This class
+  typedef HybridGaussianJunctionTree This;     ///< This class
   typedef boost::shared_ptr<This> shared_ptr;  ///< Shared pointer to this class
 
   /**
@@ -65,7 +65,7 @@ class GTSAM_EXPORT HybridJunctionTree
    * named constructor instead.
    * @return The elimination tree
    */
-  HybridJunctionTree(const HybridEliminationTree& eliminationTree);
+  HybridGaussianJunctionTree(const HybridEliminationTree& eliminationTree);
 };
 
 }  // namespace gtsam
diff --git a/gtsam/hybrid/hybrid.i b/gtsam/hybrid/hybrid.i
index 612f3abc5..94eaa88b2 100644
--- a/gtsam/hybrid/hybrid.i
+++ b/gtsam/hybrid/hybrid.i
@@ -98,15 +98,15 @@ class HybridBayesNet {
       const gtsam::DotWriter& writer = gtsam::DotWriter()) const;
 };
 
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
-class GaussianHybridFactorGraph {
-  GaussianHybridFactorGraph();
-  GaussianHybridFactorGraph(const gtsam::HybridBayesNet& bayesNet);
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+class HybridGaussianFactorGraph {
+  HybridGaussianFactorGraph();
+  HybridGaussianFactorGraph(const gtsam::HybridBayesNet& bayesNet);
 
   // Building the graph
   void push_back(const gtsam::HybridFactor* factor);
   void push_back(const gtsam::HybridConditional* conditional);
-  void push_back(const gtsam::GaussianHybridFactorGraph& graph);
+  void push_back(const gtsam::HybridGaussianFactorGraph& graph);
   void push_back(const gtsam::HybridBayesNet& bayesNet);
   void push_back(const gtsam::HybridBayesTree& bayesTree);
   void push_back(const gtsam::GaussianMixtureFactor* gmm);
@@ -120,13 +120,13 @@ class GaussianHybridFactorGraph {
   const gtsam::HybridFactor* at(size_t i) const;
 
   void print(string s = "") const;
-  bool equals(const gtsam::GaussianHybridFactorGraph& fg, double tol = 1e-9) const;
+  bool equals(const gtsam::HybridGaussianFactorGraph& fg, double tol = 1e-9) const;
 
   gtsam::HybridBayesNet* eliminateSequential();
   gtsam::HybridBayesNet* eliminateSequential(
       gtsam::Ordering::OrderingType type);
   gtsam::HybridBayesNet* eliminateSequential(const gtsam::Ordering& ordering);
-  pair<gtsam::HybridBayesNet*, gtsam::GaussianHybridFactorGraph*>
+  pair<gtsam::HybridBayesNet*, gtsam::HybridGaussianFactorGraph*>
   eliminatePartialSequential(const gtsam::Ordering& ordering);
 
   gtsam::HybridBayesTree* eliminateMultifrontal();
@@ -134,7 +134,7 @@ class GaussianHybridFactorGraph {
       gtsam::Ordering::OrderingType type);
   gtsam::HybridBayesTree* eliminateMultifrontal(
       const gtsam::Ordering& ordering);
-  pair<gtsam::HybridBayesTree*, gtsam::GaussianHybridFactorGraph*>
+  pair<gtsam::HybridBayesTree*, gtsam::HybridGaussianFactorGraph*>
   eliminatePartialMultifrontal(const gtsam::Ordering& ordering);
 
   string dot(
diff --git a/gtsam/hybrid/tests/Switching.h b/gtsam/hybrid/tests/Switching.h
index 77d8182c8..c081b8e87 100644
--- a/gtsam/hybrid/tests/Switching.h
+++ b/gtsam/hybrid/tests/Switching.h
@@ -18,8 +18,8 @@
 
 #include <gtsam/base/Matrix.h>
 #include <gtsam/discrete/DecisionTreeFactor.h>
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/GaussianMixtureFactor.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/inference/Symbol.h>
 #include <gtsam/linear/JacobianFactor.h>
 
@@ -29,10 +29,10 @@ using gtsam::symbol_shorthand::C;
 using gtsam::symbol_shorthand::X;
 
 namespace gtsam {
-inline GaussianHybridFactorGraph::shared_ptr makeSwitchingChain(
+inline HybridGaussianFactorGraph::shared_ptr makeSwitchingChain(
     size_t n, std::function<Key(int)> keyFunc = X,
     std::function<Key(int)> dKeyFunc = C) {
-  GaussianHybridFactorGraph hfg;
+  HybridGaussianFactorGraph hfg;
 
   hfg.add(JacobianFactor(keyFunc(1), I_3x3, Z_3x1));
 
@@ -51,7 +51,7 @@ inline GaussianHybridFactorGraph::shared_ptr makeSwitchingChain(
     }
   }
 
-  return boost::make_shared<GaussianHybridFactorGraph>(std::move(hfg));
+  return boost::make_shared<HybridGaussianFactorGraph>(std::move(hfg));
 }
 
 inline std::pair<KeyVector, std::vector<int>> makeBinaryOrdering(
diff --git a/gtsam/hybrid/tests/testGaussianHybridFactorGraph.cpp b/gtsam/hybrid/tests/testGaussianHybridFactorGraph.cpp
index 853353278..8ff959d74 100644
--- a/gtsam/hybrid/tests/testGaussianHybridFactorGraph.cpp
+++ b/gtsam/hybrid/tests/testGaussianHybridFactorGraph.cpp
@@ -10,7 +10,7 @@
  * -------------------------------------------------------------------------- */
 
 /*
- *  @file testGaussianHybridFactorGraph.cpp
+ *  @file testHybridGaussianFactorGraph.cpp
  *  @date Mar 11, 2022
  *  @author Fan Jiang
  */
@@ -20,7 +20,6 @@
 #include <gtsam/discrete/DecisionTreeFactor.h>
 #include <gtsam/discrete/DiscreteKey.h>
 #include <gtsam/discrete/DiscreteValues.h>
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
 #include <gtsam/hybrid/GaussianMixtureConditional.h>
 #include <gtsam/hybrid/GaussianMixtureFactor.h>
 #include <gtsam/hybrid/HybridBayesNet.h>
@@ -29,7 +28,8 @@
 #include <gtsam/hybrid/HybridDiscreteFactor.h>
 #include <gtsam/hybrid/HybridFactor.h>
 #include <gtsam/hybrid/HybridGaussianFactor.h>
-#include <gtsam/hybrid/HybridISAM.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+#include <gtsam/hybrid/HybridGaussianISAM.h>
 #include <gtsam/inference/BayesNet.h>
 #include <gtsam/inference/DotWriter.h>
 #include <gtsam/inference/Key.h>
@@ -57,25 +57,11 @@ using gtsam::symbol_shorthand::D;
 using gtsam::symbol_shorthand::X;
 using gtsam::symbol_shorthand::Y;
 
-#ifdef HYBRID_DEBUG
-#define BOOST_STACKTRACE_GNU_SOURCE_NOT_REQUIRED
-
-#include <signal.h>  // ::signal, ::raise
-
-#include <boost/stacktrace.hpp>
-
-void my_signal_handler(int signum) {
-  ::signal(signum, SIG_DFL);
-  std::cout << boost::stacktrace::stacktrace();
-  ::raise(SIGABRT);
-}
-#endif
-
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, creation) {
+TEST(HybridGaussianFactorGraph, creation) {
   HybridConditional test;
 
-  GaussianHybridFactorGraph hfg;
+  HybridGaussianFactorGraph hfg;
 
   hfg.add(HybridGaussianFactor(JacobianFactor(0, I_3x3, Z_3x1)));
 
@@ -91,8 +77,8 @@ TEST(GaussianHybridFactorGraph, creation) {
 }
 
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, eliminate) {
-  GaussianHybridFactorGraph hfg;
+TEST(HybridGaussianFactorGraph, eliminate) {
+  HybridGaussianFactorGraph hfg;
 
   hfg.add(HybridGaussianFactor(JacobianFactor(0, I_3x3, Z_3x1)));
 
@@ -102,8 +88,8 @@ TEST(GaussianHybridFactorGraph, eliminate) {
 }
 
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, eliminateMultifrontal) {
-  GaussianHybridFactorGraph hfg;
+TEST(HybridGaussianFactorGraph, eliminateMultifrontal) {
+  HybridGaussianFactorGraph hfg;
 
   DiscreteKey c(C(1), 2);
 
@@ -119,8 +105,8 @@ TEST(GaussianHybridFactorGraph, eliminateMultifrontal) {
 }
 
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, eliminateFullSequentialEqualChance) {
-  GaussianHybridFactorGraph hfg;
+TEST(HybridGaussianFactorGraph, eliminateFullSequentialEqualChance) {
+  HybridGaussianFactorGraph hfg;
 
   DiscreteKey c1(C(1), 2);
 
@@ -143,8 +129,8 @@ TEST(GaussianHybridFactorGraph, eliminateFullSequentialEqualChance) {
 }
 
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, eliminateFullSequentialSimple) {
-  GaussianHybridFactorGraph hfg;
+TEST(HybridGaussianFactorGraph, eliminateFullSequentialSimple) {
+  HybridGaussianFactorGraph hfg;
 
   DiscreteKey c1(C(1), 2);
 
@@ -171,8 +157,8 @@ TEST(GaussianHybridFactorGraph, eliminateFullSequentialSimple) {
 }
 
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, eliminateFullMultifrontalSimple) {
-  GaussianHybridFactorGraph hfg;
+TEST(HybridGaussianFactorGraph, eliminateFullMultifrontalSimple) {
+  HybridGaussianFactorGraph hfg;
 
   DiscreteKey c1(C(1), 2);
 
@@ -204,8 +190,8 @@ TEST(GaussianHybridFactorGraph, eliminateFullMultifrontalSimple) {
 }
 
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, eliminateFullMultifrontalCLG) {
-  GaussianHybridFactorGraph hfg;
+TEST(HybridGaussianFactorGraph, eliminateFullMultifrontalCLG) {
+  HybridGaussianFactorGraph hfg;
 
   DiscreteKey c(C(1), 2);
 
@@ -240,8 +226,8 @@ TEST(GaussianHybridFactorGraph, eliminateFullMultifrontalCLG) {
  * This test is about how to assemble the Bayes Tree roots after we do partial
  * elimination
  */
-TEST(GaussianHybridFactorGraph, eliminateFullMultifrontalTwoClique) {
-  GaussianHybridFactorGraph hfg;
+TEST(HybridGaussianFactorGraph, eliminateFullMultifrontalTwoClique) {
+  HybridGaussianFactorGraph hfg;
 
   hfg.add(JacobianFactor(X(0), I_3x3, X(1), -I_3x3, Z_3x1));
   hfg.add(JacobianFactor(X(1), I_3x3, X(2), -I_3x3, Z_3x1));
@@ -290,7 +276,7 @@ TEST(GaussianHybridFactorGraph, eliminateFullMultifrontalTwoClique) {
   GTSAM_PRINT(ordering_full);
 
   HybridBayesTree::shared_ptr hbt;
-  GaussianHybridFactorGraph::shared_ptr remaining;
+  HybridGaussianFactorGraph::shared_ptr remaining;
   std::tie(hbt, remaining) = hfg.eliminatePartialMultifrontal(ordering_full);
 
   GTSAM_PRINT(*hbt);
@@ -309,7 +295,7 @@ TEST(GaussianHybridFactorGraph, eliminateFullMultifrontalTwoClique) {
 
 /* ************************************************************************* */
 // TODO(fan): make a graph like Varun's paper one
-TEST(GaussianHybridFactorGraph, Switching) {
+TEST(HybridGaussianFactorGraph, Switching) {
   auto N = 12;
   auto hfg = makeSwitchingChain(N);
 
@@ -381,7 +367,7 @@ TEST(GaussianHybridFactorGraph, Switching) {
   GTSAM_PRINT(ordering_full);
 
   HybridBayesTree::shared_ptr hbt;
-  GaussianHybridFactorGraph::shared_ptr remaining;
+  HybridGaussianFactorGraph::shared_ptr remaining;
   std::tie(hbt, remaining) = hfg->eliminatePartialMultifrontal(ordering_full);
 
   // GTSAM_PRINT(*hbt);
@@ -417,7 +403,7 @@ TEST(GaussianHybridFactorGraph, Switching) {
 
 /* ************************************************************************* */
 // TODO(fan): make a graph like Varun's paper one
-TEST(GaussianHybridFactorGraph, SwitchingISAM) {
+TEST(HybridGaussianFactorGraph, SwitchingISAM) {
   auto N = 11;
   auto hfg = makeSwitchingChain(N);
 
@@ -473,7 +459,7 @@ TEST(GaussianHybridFactorGraph, SwitchingISAM) {
   GTSAM_PRINT(ordering_full);
 
   HybridBayesTree::shared_ptr hbt;
-  GaussianHybridFactorGraph::shared_ptr remaining;
+  HybridGaussianFactorGraph::shared_ptr remaining;
   std::tie(hbt, remaining) = hfg->eliminatePartialMultifrontal(ordering_full);
 
   // GTSAM_PRINT(*hbt);
@@ -499,10 +485,10 @@ TEST(GaussianHybridFactorGraph, SwitchingISAM) {
   }
 
   auto new_fg = makeSwitchingChain(12);
-  auto isam = HybridISAM(*hbt);
+  auto isam = HybridGaussianISAM(*hbt);
 
   {
-    GaussianHybridFactorGraph factorGraph;
+    HybridGaussianFactorGraph factorGraph;
     factorGraph.push_back(new_fg->at(new_fg->size() - 2));
     factorGraph.push_back(new_fg->at(new_fg->size() - 1));
     isam.update(factorGraph);
@@ -512,7 +498,7 @@ TEST(GaussianHybridFactorGraph, SwitchingISAM) {
 }
 
 /* ************************************************************************* */
-TEST(GaussianHybridFactorGraph, SwitchingTwoVar) {
+TEST(HybridGaussianFactorGraph, SwitchingTwoVar) {
   const int N = 7;
   auto hfg = makeSwitchingChain(N, X);
   hfg->push_back(*makeSwitchingChain(N, Y, D));
@@ -582,7 +568,7 @@ TEST(GaussianHybridFactorGraph, SwitchingTwoVar) {
   }
   {
     HybridBayesNet::shared_ptr hbn;
-    GaussianHybridFactorGraph::shared_ptr remaining;
+    HybridGaussianFactorGraph::shared_ptr remaining;
     std::tie(hbn, remaining) =
         hfg->eliminatePartialSequential(ordering_partial);
 
diff --git a/gtsam/inference/inference.i b/gtsam/inference/inference.i
index e8d918a1d..fbdd70fdf 100644
--- a/gtsam/inference/inference.i
+++ b/gtsam/inference/inference.i
@@ -9,7 +9,7 @@ namespace gtsam {
 #include <gtsam/nonlinear/NonlinearFactorGraph.h>
 #include <gtsam/symbolic/SymbolicFactorGraph.h>
 #include <gtsam/discrete/DiscreteFactorGraph.h>
-#include <gtsam/hybrid/GaussianHybridFactorGraph.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 
 #include <gtsam/inference/Key.h>
 
@@ -107,36 +107,36 @@ class Ordering {
 
   template <
       FACTOR_GRAPH = {gtsam::NonlinearFactorGraph, gtsam::DiscreteFactorGraph,
-                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::GaussianHybridFactorGraph}>
+                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::HybridGaussianFactorGraph}>
   static gtsam::Ordering Colamd(const FACTOR_GRAPH& graph);
 
   template <
       FACTOR_GRAPH = {gtsam::NonlinearFactorGraph, gtsam::DiscreteFactorGraph,
-                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::GaussianHybridFactorGraph}>
+                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::HybridGaussianFactorGraph}>
   static gtsam::Ordering ColamdConstrainedLast(
       const FACTOR_GRAPH& graph, const gtsam::KeyVector& constrainLast,
       bool forceOrder = false);
 
   template <
       FACTOR_GRAPH = {gtsam::NonlinearFactorGraph, gtsam::DiscreteFactorGraph,
-                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::GaussianHybridFactorGraph}>
+                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::HybridGaussianFactorGraph}>
   static gtsam::Ordering ColamdConstrainedFirst(
       const FACTOR_GRAPH& graph, const gtsam::KeyVector& constrainFirst,
       bool forceOrder = false);
 
   template <
       FACTOR_GRAPH = {gtsam::NonlinearFactorGraph, gtsam::DiscreteFactorGraph,
-                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::GaussianHybridFactorGraph}>
+                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::HybridGaussianFactorGraph}>
   static gtsam::Ordering Natural(const FACTOR_GRAPH& graph);
 
   template <
       FACTOR_GRAPH = {gtsam::NonlinearFactorGraph, gtsam::DiscreteFactorGraph,
-                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::GaussianHybridFactorGraph}>
+                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::HybridGaussianFactorGraph}>
   static gtsam::Ordering Metis(const FACTOR_GRAPH& graph);
 
   template <
       FACTOR_GRAPH = {gtsam::NonlinearFactorGraph, gtsam::DiscreteFactorGraph,
-                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::GaussianHybridFactorGraph}>
+                      gtsam::SymbolicFactorGraph, gtsam::GaussianFactorGraph, gtsam::HybridGaussianFactorGraph}>
   static gtsam::Ordering Create(gtsam::Ordering::OrderingType orderingType,
                                 const FACTOR_GRAPH& graph);
 
diff --git a/python/gtsam/tests/test_HybridFactorGraph.py b/python/gtsam/tests/test_HybridFactorGraph.py
index 895c9e14e..07a8178e6 100644
--- a/python/gtsam/tests/test_HybridFactorGraph.py
+++ b/python/gtsam/tests/test_HybridFactorGraph.py
@@ -20,8 +20,8 @@ from gtsam.symbol_shorthand import C, X
 from gtsam.utils.test_case import GtsamTestCase
 
 
-class TestGaussianHybridFactorGraph(GtsamTestCase):
-    """Unit tests for GaussianHybridFactorGraph."""
+class TestHybridGaussianFactorGraph(GtsamTestCase):
+    """Unit tests for HybridGaussianFactorGraph."""
 
     def test_create(self):
         """Test contruction of hybrid factor graph."""
@@ -36,13 +36,13 @@ class TestGaussianHybridFactorGraph(GtsamTestCase):
 
         gmf = gtsam.GaussianMixtureFactor.FromFactors([X(0)], dk, [jf1, jf2])
 
-        hfg = gtsam.GaussianHybridFactorGraph()
+        hfg = gtsam.HybridGaussianFactorGraph()
         hfg.add(jf1)
         hfg.add(jf2)
         hfg.push_back(gmf)
 
         hbn = hfg.eliminateSequential(
-            gtsam.Ordering.ColamdConstrainedLastGaussianHybridFactorGraph(
+            gtsam.Ordering.ColamdConstrainedLastHybridGaussianFactorGraph(
                 hfg, [C(0)]))
 
         # print("hbn = ", hbn)