tfishell: What about privacy?
Elenarie: Why would this be an issue? Are you ashamed of yourself and your actions on some websites / Internet places?
Others have responded rather eloquently. Sadly, my response won't be quite as:
Fuck. Right. Off.
That argument is not too many steps removed from the whole "if you've got nothing to hide..." bullshit that people spout when almost Orwellian security measures are suggested.
As has been said, the potential problems far outweigh the removal of a couple of trolls. The internet, for better or worse, is one of the few places where true freedom of speech exists. It exists because of the very anonymity you seem to despise so much.
I don't tell everyone I meet and talk to in the street my name. I don't tell people I see often in the course of work, or shopping, or whatever my name, unless it's needed.
As far as I can figure it, only a complete imbecile would want anything like what you propose to actually be implemented.