How to rename Music Library

You can rename your music library just as you would rename any other Mac file or folder.

Rename files, folders, and disks on Mac - Apple Support

Make sure you do not change the filename suffix. It must remain .musiclibrary

While you can rename your music library, you can also direct the Music app to open a different library when you launch it. Apple's guidance for that is here: Use multiple libraries in Music on Mac - Apple Support