How to use Asset Action Utility to batch rename files without breaking references?

I’m currently using this script to batch rename files: BatchReplaceSelected posted by anonymous | blueprintUE | PasteBin For Unreal Engine

However, when I use it with a plugin “Menu System Pro” made from blueprints, many reference aren’t updated and it breaks the whole thing.

The workaround is current to rename the assets manually.

The “Rename Asset” message didn’t work either:

Is there any way to use a function that replace the name and references correctly?