Surely if the cause is important to them they should sign with their legal name.
If I signed an ink-and-paper petition as CuddleBunny227 it would be rightly disregarded and stricken even if I insisted that was my username on Reddit. Does that change if it's "on the Internet"?
If CuddleBunny227 is your stage name that you release music under and people know you as, you should probably use it so people recognise the name. It's ultimately a personal choice of whether you wanna doxx your real name or not, and many online artists prefer not to, in which case putting both names alongside would be unacceptable
This is HN, we don't really need witticisms at the top of the comment section.