1. You need to do this on an account where its characters are on a high population server with free transfers.
2. Go to the realm you are going to transfer your character and make a character with the same name.
3. Transfer your character. You will get to change your name here.
4. Now call in billing and tell them that the free transfer service transferred the wrong character somehow. (make sure you delete the char with your old name beforehand.)
5. Now you will get your character transferred back with your new name.
It might take a while when doing all of this so i suggest that you don't do it on your main unless you want to wait a week or two to play.
And make sure you don't log in your character when it is on the new realm and don't trade people / get on AH.
I have done this to a couple of characters already so have fun.