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 ;-)
Its nice but to me Tyler Braxon sounds better.
Braxton Tyler sounds better. The other way around sounds like a first and last name rather than a first and middle
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..