Force Rename of GameObject in Hierarchy

The script posted in the old answer no longer works in newer unity versions. Use this instead:

     using UnityEngine;
     using UnityEditor;
     using System.Reflection;
      
     public class ObjClone : EditorWindow
     {
      
         // Add menu named "My Window" to the Window menu
         [MenuItem("Window/ObjClone")]
         static void Init()
         {
             // Get existing open window or if none, make a new one:
             ObjClone window = (ObjClone)EditorWindow.GetWindow(typeof(ObjClone));
             window.Show();
         }
      
         GameObject g;
         GameObject clone;
         volatile bool triggerRename;
         private static double renameTime;
      
         void OnGUI()
         {
             g = (GameObject)EditorGUILayout.ObjectField(g, typeof(GameObject), true);
             if (GUILayout.Button("Clone"))
             {
                 clone = Instantiate<GameObject>(g);
      
                 EditorApplication.update += EngageRenameMode;
                 renameTime = EditorApplication.timeSinceStartup + 0.4d;
                 EditorApplication.ExecuteMenuItem("Window/General/Hierarchy");
                 Selection.activeGameObject = clone;
             }
         }
      
         private void EngageRenameMode()
         {
             if (EditorApplication.timeSinceStartup >= renameTime)
             {
                 EditorApplication.update -= EngageRenameMode;
                 var e = new Event { keyCode = KeyCode.F2, type = EventType.KeyDown }; // or Event.KeyboardEvent("f2");
                 EditorWindow.focusedWindow.SendEvent(e);
             }
         }
     }
 

OBSOLETE:

Ok. Took me some time, but here you go:

 using UnityEngine;
 using UnityEditor;
 using System.Reflection;
 
 public class ObjClone : EditorWindow
 {
 
     // Add menu named "My Window" to the Window menu
     [MenuItem("Window/ObjClone")]
     static void Init()
     {
         // Get existing open window or if none, make a new one:
         ObjClone window = (ObjClone)EditorWindow.GetWindow(typeof(ObjClone));
         window.Show();
     }
 
     GameObject g;
     GameObject clone;
     volatile bool triggerRename;
     private static double renameTime;
 
     void OnGUI()
     {
         g = (GameObject)EditorGUILayout.ObjectField(g, typeof(GameObject), true);
         if (GUILayout.Button("Clone"))
         {
             clone = Instantiate<GameObject>(g);
 
             EditorApplication.update += EngageRenameMode;
             renameTime = EditorApplication.timeSinceStartup + 0.4d;
             EditorApplication.ExecuteMenuItem("Window/Hierarchy");
             Selection.activeGameObject = clone;
         }
     }
 
     private void EngageRenameMode()
     {
         if (EditorApplication.timeSinceStartup >= renameTime)
         {
             EditorApplication.update -= EngageRenameMode;
             var type = typeof(EditorWindow).Assembly.GetType("UnityEditor.SceneHierarchyWindow");
             var hierarchyWindow = EditorWindow.GetWindow(type);
             var rename = type.GetMethod("RenameGO", BindingFlags.Instance | BindingFlags.NonPublic);
             rename.Invoke(hierarchyWindow, null);
         }
     }
 }