You can send private messages on the forum, but I believe it will still be a user name.
I did sign up for the forum, but never got a password and gave up trying in the end.
The only time you will see a real name is if the person has set up their account for it to show.
For example, if you click twice on my user name, you will see that I'm female, but not my real name.
But if you click twice on say Jarvo's user name, it does say what his real name is, as that is the way his account is set up.
As sir Bob has mentioned, there will be a message functionality in the New World