Yeah, this one is pretty easy. After you rename your drive (volume name) the file path to all of the files is going to change. So it will be something like:
old: /Volumes/MyBook/
new /Volumes/Realy_Cool_Drive_Name/
So, naturally, when you change the path to all of the files, MC can no longer find them. The solution is to use the Rename, Move, and Copy files tool to update all of the file pointers to point to the new location. Here's the wiki page on the RM&C tool:
https://wiki.jriver.com/index.php/Rename,_Move,_and_Copy_FilesRM&C is a big tool that can do a lot. What you want to do in this case is use UPDATE ONLY mode. This mode just changes the file pointers and doesn't try to rename any files on disk. Second, you want to use the Find and Replace template at the bottom of the tool. This will let you simply substitute the New Drive Name for the Old Drive Name.
Notice that RM&C has a PREVIEW WINDOW on the right. This will show you what it's going to do BEFORE you press OK. Use the Preview Window to make sure you are doing the right thing. If it looks wrong, make some adjustments and look again. Don't press OK until the preview looks right.
Do ONE FILE as a test. Once that works, do a few more files. Maybe a whole album. Once that works, you can move on to more files; maybe everything else at once.
Good luck!
Brian.