Well, actually, Anonymous didn't really chose the name - it was a joke made on default "Anonymous" username on 4chan. And it really grew somehow organically into this point.
That's what I don't like about people saying "You are not true Anonymous". First hackers under the name "Anonymous" posted other people MySpace passwords on 4chan and put blinking lights on epilepsy website. And the whole scientology movement was first meant as a joke, as a reaction to the leaked Tom Cruise video.
Really, people calling other people "not true Anonymous" are hypocritical. I think.