So I changed my Gamertag tag to Rez Faith and that's all I put and then I opened up...

Since someone else has the same gamertag, a suffix was added to yours to differentiate you. In areas that haven't been updated to work with the new gamertag system, that's how it will show.

I am listed on my xbox as one gamertag, but when I try to log in on the computer it comes up with a generic gamertag. I can't change anything, and if I try to change the generic tag to my tag on the xbox, it tells me that name is already taken. Also, the
generic tag does not have any of the games that I play on it. I used to be able to log in with my old tag, but for some reason it has all changed.

Hello, im trying to change my Gamertag, im from Spain, my xbox region is Spain and language Spanish, when im trying to change my Gamertag i put the information of my credit card and my other information, then when i click in accept i cant change the name
because one error is open... I put all the information good and i have money in the credit card but its impossible.. Please i need to change my gamertag

The best way would be to change the tag to something else. That would open it up for use on a new account. Otherwise the Microsoft account would have to be closed and it can take some time for the tag to be freed up.

There's also been a new policy change so you can have a gamertag even if it's already been taken. https://support.xbox.com/my-account/manage-gamertag-and-profile/gamertag-updates-faq

I guess I'm not understanding the NEED to move the gamertag. I can see how doing so could open up a big can of worms. You would need to prove the original account with the gamer tag you want transferred belongs to you. If you can do that why not just log
into the account and change the gamertag and then change it over on the "new" account, but if you have access to the original account why move it at all.