Invented name, likely derived from Braxton meaning Brocks town.
Brextyn is a modern American coinage, likely created by blending the surname Braxton with the popular '-tyn' suffix. Braxton itself is an English locational surname meaning 'Brock's settlement' or 'badger's town.'
Less common today
Brextyn isn't in the latest US Top 1000. It last peaked at #4,845 in 2020.
US births per 5-year period, 1990βpresent (SSA data).