If I’m following this, it sounds like the computer filenames use the artist names, but that the “ID3 tags” for the files/songs (artist, album, title, year, genre), which WMP and players like the Clip use to display that information and which are contained within the computer files, have not been filled in.
You need, then, to use a tag editor like MP3Tag or The Godfather, to fill that information in. You also can do it more manually by right clicking (on your computer) on the file, and then Properties, and Details (this is on Windows Vista; it’s similar on XP (IIRC, you then click on Advanced)), and filling the info. in.
I hope this helps and makes sense–it’s easy to do, in the end. A tag editor is recommended, for ease.
Note that if you rip your files yourself from a CD, many rippers will search out on the Internet and fill this info. in automatically (which you then can edit), if you choose this option–a great timesaver.