Whilst I also hate Twitter with a passion, an interesting whinge from a friend that owns a small business made me look into it a bit more.
There are actually people out there registering a million fucking Twitter address just to squat on them (it's like a lamer, less valuable version of domain squatting), you should probably register your name, your regular alias, and maybe even your site name, just to make sure some other arsehole doesn't...
What's even sadder is that some of these guys are even making all of their squatted accounts follow each other, so they'll bullshit you and say it's already got followers on the account, so they've made it valuable and you should pay them for it.
The dumbest thing is that Twitter doesn't seem to do anything to stop this.