Sure, that's cake. Select the files and open the Rename, Move, and Copy tool.
1. In the top pull down list, select the action you want. You want to rename files, so select Rename.
2. Check the box next to Directories.
3. If the base path isn't going to change, Erase the Base Path. So, if your music is in something like S:\Music\Artist Name\Album Name and you aren't going to change the S:\Music part, erase the Base Path and it will stay as is.
4. In the Rule box fill in: [Artist]\[Album]\
This will tell it to keep your current rule of organizing by Artist and then Album. Note that for compilation albums you probably want ot use [Album Artist (auto)] instead of [Artist]. Otherwise, compilations will get broken up into one directory per artist on the compilation.
5. Check the box next to Filename.
6. Fill in the filename for how you want it named. If you like your existing filenames, uncheck the box in the step above and don't touch this field. However, my recommendation is to change your filenames slightly. I like to have names like this:
01_01_First_Song_From_First_Disc_Here.flac
01_02_Second_Song_First_Disc.flac
02_01_First Song_Second Disc.flac
02_02_Second_Song_Second_disc.flac
That way they sort properly in the file system by Disc number, then song number, and of course you still see the song name. So to do this you fill out the filename template like this:
padnumber([Disc #],2)_[Track #]_[Name]
The padnumber part makes the disc # two digits. I like the consistency of two digits. If you don't care then just:
[Disc #]_[Track #]_[Name]
7. Look at the Preview pane on the right. It will show you exactly what it's going to do. Hover over the files to see the exact path they are going to be renamed to. Adjust the Directory Rule and/or Filename rule as necessary to get it named exactly as you want it.
8. When it all looks good, press OK and it will rename your files as you have told it to.
I suggest trying this on a small group of files first; maybe 2 or 3. Then when it works, you can do a bunch at once if you are comfortable. Or an album at a time, or whatever you like.
Good luck!
Brian.