Like m-c did before, create parent directories if needed on m-m.

lib/nerdtree/path.vim

@@ -663,6 +663,8 @@ function! s:Path.rename(newPath)
         throw "NERDTree.InvalidArgumentsError: Invalid newPath for renaming = ". a:newPath
     endif
 
+    call s:Path.createParentDirectories(a:newPath)
+
     let success =  rename(self.str(), a:newPath)
     if success != 0
         throw "NERDTree.PathRenameError: Could not rename: '" . self.str() . "'" . 'to:' . a:newPath

nerdtree_plugin/fs_menu.vim

@@ -158,6 +158,7 @@ function! NERDTreeMoveNode()
         let bufnum = bufnr("^".curNode.path.str()."$")
 
         call curNode.rename(newNodePath)
+        call b:NERDTree.root.refresh()
         call NERDTreeRender()
 
         "if the node is open in a buffer, ask the user if they want to