I loved Braxton too but Everytime I told someone we were naming our son braxton they would say oh braxton hicks... made me upset so we changed it..
Braxton Tyler sounds better. The other way around sounds like a first and last name rather than a first and middle
Its nice but to me Tyler Braxon sounds better.
Personally I don't like Braxon but that is because I'm a teacher and have a student named Braxton who isn't exactly fun to teach ;-)