The real name policy has huge benefits. I'm not constantly bombarded by fake friend requests like I am on Twitter, Skype, or any other platform which allows random usernames. Even more importantly, I can easily find the people in my life without having to go through an awkward song and dance. If I'm working on a project with someone, I can immediately find them and message them without worrying that it's some random imposter or some such.
Facebook is a platform designed for digitizing your real world relationships, not for accumulating thousands of "followers." There's a reason they limit you to 5,000 friends. People who are trying to disconnect their Facebook identity from their real world identity are not using Facebook the way it's meant to be used and should probably just leave it.
That being said, Facebook could definitely do a better job of making it easier for people to prove that a name is their everyday name even when it's not their legal name.
I fully expect to lose a lot of karma over this comment, but I'd love to hear an argument over why access to Facebook is a right together with your down vote.