Updated with feedback

com.unity.shadergraph/Editor/Drawing/MaterialGraphEditWindow.cs

                     graphEditorView = new GraphEditorView(this, materialGraph)
                     {
                         persistenceKey = selectedGuid,
-                        assetName = asset.name
+                        assetName = asset.name.Split('/').Last()
                     };
                     m_ColorSpace = PlayerSettings.colorSpace;
                 }
                 graphEditorView = new GraphEditorView(this, m_GraphObject.graph as AbstractMaterialGraph)
                 {
                     persistenceKey = selectedGuid,
-                    assetName = asset.name
+                    assetName = asset.name.Split('/').Last()
                 };
                 graphEditorView.RegisterCallback<GeometryChangedEvent>(OnGeometryChanged);
 

com.unity.shadergraph/Editor/Drawing/Views/GraphEditorView.cs

 
         public string assetName
         {
-            get { return m_BlackboardProvider.blackboard.title; }
+            get { return m_BlackboardProvider.assetName; }
-                m_BlackboardProvider.blackboard.title = value.Split('/').Last();
-                m_MasterPreviewView.assetName = value.Split('/').Last();
+                m_BlackboardProvider.assetName = value;
+                m_MasterPreviewView.assetName = value;
             }
         }