Previous fix didn't work if you don't Save() the document +don't publish copies.

src/Umbraco.Core/Services/ContentService.cs

@@ -976,10 +976,14 @@ namespace Umbraco.Core.Services
         /// <param name="userId">Optional Id of the User copying the Content</param>
         /// <returns>The newly created <see cref="IContent"/> object</returns>
         public IContent Copy(IContent content, int parentId, bool relateToOriginal, int userId = -1)
-		{
+        {
 			var copy = ((Content)content).Clone();
 			copy.ParentId = parentId;
 
+            // A copy should never be set to published
+            // automatically even if the original was
+            this.UnPublish(copy);
+
 			if (Copying.IsRaisedEventCancelled(new CopyEventArgs<IContent>(content, copy, parentId), this))
 				return null;
 
@@ -987,7 +991,7 @@ namespace Umbraco.Core.Services
 			using (var repository = _repositoryFactory.CreateContentRepository(uow))
 			{
 				SetWriter(content, userId);
-
+			    
 				repository.AddOrUpdate(copy);
 				uow.Commit();
 

src/Umbraco.Web/umbraco.presentation/umbraco/ActionHandlers/umbEnsureUniqueName.cs

@@ -67,6 +67,7 @@ namespace umbraco.ActionHandlers
 					LogHelper.Debug<umbEnsureUniqueName>("Title changed from '" + documentObject.Text + "' to '" + currentName + "' for document  id" + documentObject.Id);
                     
                     documentObject.Text = currentName;
+                    documentObject.Save();
 
                     return true;
                 }