I've noticed that hardly anybody uses an underscore character in their Twitter name. So, I've changed mine from William_Sky to Skyvington.
Within the system, this modification appears to be transparent. So, I don't have to notify anybody in any way whatsoever.
It might look a little pretentious of me to refer to myself by a simple surname... like Charlemagne. In fact, it's great to have a surname that is so rare (maybe due to a spelling error committed by an ancestor) that no other user of Twitter has ever seized it. Now, if some other Skyvington decides to use Twitter, I'm afraid that he or she might be obliged to decline their identity by adopting a precise name such as Emmanuelle_Skyvington or François_Skyvington, for example. Sorry about that. But, as they say in the Bible: First come, first served! Besides, I get a kick out of thinking of myself (once again, as they say in the Bible) as a patriarch... like, say, Mr Moses, Esquire.