I had to do this at one stage with a small group of files, in that case, I stored the filepaths of every file, as well as create-date and filesize every time I polled.
Then every subsequent poll, I was able to detect files that are now 'missing' from the last time I polled. Then, I would cross check time created and filesize to detect if some of the newer files match some of the missing files. If I get a match, I assume a rename.
Please note however, it may not be safe / 100% accurate; you may have multiple files with the same create date and filesize etc. In my case, it was use generated photographs, I was able to also check exif data as a final verification. Depending on your situation, you may have other pieces of data to verify against.