Bronson \b-ron-son, br(o)-nson\ as a boy's name is pronounced BRAHN-sun. It is of Middle English origin, and the meaning of Bronson is "son of the brown man". Actors Charles Bronson, Bronson Rinchot. Bronson has 6 variant forms: Bron, Bronnson, Bronsen, Bronsin, Bronsonn and Bronsson. Baby names that sound like Bronson are Branson, Branston and Bransen.