You can use a program, such as the free
Mp3Tag, to edit the ID info embedded in the file. They have versions for Windows (there's even an old version that works back to Windows 95!) and Mac OSX. It's easy to use.
Renaming the files is a good idea, though. If something happens and the ID data gets wiped, you'll still know what it is. You can always dig up the rest of the info from that.