Curious which of those Bach entries you think should be the short name? I'd want "J. S. Bach", but I'm guessing someone not familiar with Baroque and Classical music would want just "Bach". That's because there is also a C. P. E. Bach, W. F. Bach, J. C. F. Bach, J. C. Bach, and of course P. D. Q. Bach . They're less well-known, though.
I'm not sure how we'd resolve those disputes. Unlike most of the data in MB, there isn't an authoritative source (album booklet, score, etc.) to point to. And this sounds like something fairly contentious.
I guess maybe it'd work like tags, where they're voted on. Especially if the tagger would always listen to your vote, even if you're in the minority (though then you have to make a ranking as your vote, not just simple approval). This sounds like a lot of complexity.
Also, having non-stable names strikes me as a problem: you're going to have to routinely retag the entire artist, otherwise he/she may get split in your music library (when the short name changes from "Bach" to "J. S. Bach", etc.).