Very simple method that my brother thought of, we tried it out and it worked.
Basically a week or so ago we scammed an account with a 70 mage on it that my brother wanted to keep, he wanted the last name so he can make a new account with the same name to transfer the mage for more security.
The realm I play on is an RP realm and he thought, if you make a character on a RP realm with a ridiculous name like "theorcwar" for example you can get reported and if it goes through the next time you log on you'll get prompted to change your name along with an email telling you what happened. We thought the email might contain the full name as emails for certain circumstances do.
So we tried it, he made a character on my realm with this name, leveled it to 6 and I reported it. We logged off and when I came back a few hours later I had a mail from a GM (I logged with the ticket open) saying the basic "We'll look into it" message, and my brothers character had been prompted for a name change along with an email :-)
So, in short:
1. Make character on RP realm with the account you want the full name on
2. Call this character something stupid like "pwnmage", good idea to level this to around 4-6.
3. If you don't have one already, make a character on another account on the same realm with a proper name.
4. Report your stupid named character with your real named character
5. Log off (optional) and wait.
You SHOULD receive the email with the full name.
You don't receive any suspension or even account warnings for this so don't worry.