The simplest way to swap a gamertag from account to account is just to add a minimum of 800 Microsoft Points on each tag. Change the name on the account with the name you want onto your other account, then change the name of your other account to it.
Make sure not to tell anyone you're swapping your gamertag, and do it late at night. Another thing to remember is wait around a week or so if you have a bought a very good gamertag (ESPECIALLY if you paid $75 or more for it) before you swap it, or else someone might turbo your tag.
Any questions? Hit me up with a private message.