Your comments

I think the best way to handle this would probably be to have it by default let other users see who you are when you favorite their content (as everyone is used to on every other site), but to have a user setting for something along the lines of "do not let other users see when I have favorited their content" which would result in anonymous favorite notifications. I feel like that would be the best of both worlds.

I say visible by default and with the setting to hide it because I think the vast majority of users would be fine with letting an artist know that they liked something of theirs via a favorite.