If I change my gamertag on one account can I take that same name on my other account?

Okay, say on my old Xbox 360 profile my gamertag is "HELLO 01", and on my new profile my gamertag is "BONJOUR 01", Can I change "BONJOUR 01" to "SUP 01" then change my old profile's gamertag from "HELLO 01" to "BONJOUR 01" like the same day? See what I did was I created a new profile and made it Xbox live gold but now I don't want to use my new account but I want to change my old profile's gamertag to the one that my new profile has.