I'd probably use my CFC username. Quintillus, to be followed by Emperor Quintillus if I were as successful as al-Jolani. Or maybe I'd let some democratically elected form of government rule instead. Things didn't end very well for the original Emperor Quintillus, and that "other people want power too" element was likely part of the problem.
I have a few other aliases on other sites but don't like any of them as well, and if I shared my nom de plume, you, and the rest of the Internet, could figure out where I write (quite infrequently of late, and not published, essentially a blog).
No rap alias, but I keep a short document of potential band names just in case I ever pick up a guitar and find out that one guitar, slung way down low, is a one way ticket to a sold-out show.