Don't Clear Name on copied Elements, change the name to "_Copy","_Copy1","_Copy2"....

src/AddIns/DisplayBindings/WpfDesign/WpfDesign.Designer/Project/Xaml/XamlComponentService.cs

@@ -93,8 +93,22 @@ namespace ICSharpCode.WpfDesign.Designer.Xaml
 				var nameScope = _context.RootItem.Component as INameScope;
 				nameScope = NameScope.GetNameScope((DependencyObject) _context.RootItem.Component);
 				var fnd = nameScope.FindName(site.Name);
-				if (fnd != null)
+				
-					site.Name = null;
+				if (fnd != null) {
+					string newNm = site.Name + "_Copy";
+					fnd = nameScope.FindName(newNm);
+					if (fnd == null)
+						site.Name = newNm;
+					else {
+						int i = 1;
+						while (fnd != null) {
+							newNm = site.Name + "_Copy" + i;
+							fnd = nameScope.FindName(newNm);
+							i++;
+						}
+						site.Name = newNm;
+					}
+				}
 			}
 			return site;
 		}