Hi,
The easiest way to do what you’re talking about is to use MediaMover. You can download a fully-functional 30-day trial here: https://www.randomvideo.com/
If you move Avid projects a lot you’ll find the 150 bucks money well spent.
Otherwise you could use the media tool to identify all media for the project, or the console command “rename mediafiles” (I can’t quite remember the exact command) and select all the files related to the project. This is entering scary territory, especially if multiple projects are sharing media. I’d check media mover out.
Hope this helps