If you change the file names in Booster's Lab I think you still have to change the file names in the Stage folder.
As for changing the internal song names via .data ... you don't really need to, but if you want to:
1. Make sure you're using a hex editor to edit .data, and always leave a 00 at the end of your string so that it doesn't leak into another string. (But do not overwrite or move the starting position of other strings know what you're doing)
2. Rename the resources themselves (probably with Resource Hacker)
But there is no point in doing this because the only way you'd see these is by opening the game's exe.
If you're interested in using waveform sound files then you can easily use Clownacy's mod loader:
https://www.cavestory.org/forums/threads/dll-mod-loader-extra-music-formats-mod.13879/
Or with a bit more patience and finesse (and if you know where to look) you can use 20kdc's N.I.C.E. Lua mod.
Also, I'd recommend using OGGs over MP3s for quality's sake. Or FLAC/s if you're OK with big uploads. (or even WAVs if you like wasting space)