From the Super Mario Wiki
B. Coz (full name B. Costello) is a character who appears in the Game Boy Color version of Mario Tennis. He is on the Factory team. Unlike B. Coz's partner (and brother), A. Coz, he can serve and hit powerful shots. The player faces B. Coz in the Island Open. In doubles, the player faces him in the final round. In singles, B. Coz loses against Emily in the second round.
In Mario Tennis: Power Tour, which takes place several years later, he and A. Coz are revealed to be coaches at Factory. Their younger brother, Willy, is the player's final opponent in the Island Open.
B. Coz's name comes from the English word "because".