I know that most people who are saying yes will say that it will give more chance to have privacy and will stop posting insulting comments. No, however, I say, because what if using your real name is revealed on the Internet. You have to admit that human feelings urges us to feel a little nervous and will not like a bit to comment. And if your name is revealed on the Internet, it would be even easier to be hacked inside your privacy boundaries, since everybody knows your name. And what if you admit a problem, perhaps seeking advice, and has to mention somebody? And if that somebody sees your article, it would be a lot more comfy to post it anonymous.
And anyway, if people want to post very insulting comments, and somebody just reports them to the police, the cyber police will just VERY EASILY track down that person's real name.
You don't necessarily have to ban it!