From the Super Mario Wiki
B. Coz 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, 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 have become coaches at Factory.
B. Coz's name comes from the English word "because".