I thought of RealMyName, but that is kinda arrogant since there are a thousand people with my name. The other options are too long for Twitter.

I could go with RealMyName since nobody's using it. Or maybe something less abrasive like HeyMyName.

What about DistinctMyName? JobMyName? KindMyName? CruelMyName? Simply choose an adjective, perhaps a location, something to distinct you from the other homonyms.

Maybe FakeMyName would be better / funnier.