Plex should support renaming of media files.
Either through Plex UI, or by processing addition before removal.
If Plex process addition of new media before deletion, then it will reuse the existing entry.
Just moved several movies from one directory to another, and they where all deleted, then added as new titles.
A workaround for file rename would be to copy the files (renamed) and then delete the old, but it is too much work.