Okay so i use to do this all the time during the Burning Crusade and it worked almost every time, the reason it works 'almost' everytime is sometimes the GM deletes the character with the same name
1) If you have another account go to the realm of the character you want to change. If not, ask a close friend or someone you know well in game to do you a favor
2) on the account with the characters name you want to change, If you havent used your recovery that many times delete the character
3) go to your other account and make a character with the same name and level him up to at least 5 and stay logged in (have your friend level it to 5 or so and tell him to stay logged in)
4) On your account make a new character or go on an alt and open a ticket saying you want to recover a deleted character
List the characters name and realm and level and what not.
When they get to you this is where it is tough cuz sometimes they will either have the other person change their name, or they will be too lazy and flag your name and tell you that the next time you log in it will prompt you to type in a new name
Worked for like like 80% of the time x]
Good luck and i hope this works for you!