From the Super Mario Wiki
A. Coz (full name A. Costello) is a character in the Game Boy Color version of Mario Tennis, and the oldest of the three Costello brothers. Unlike his partner, B. Coz, he is a speedy player and can return almost any ball. In Singles, the player faces A. Coz in the final round of the Island Open. Like the player, it's his first time in the tournament.
In Mario Tennis: Power Tour, which takes place several years later, he and B. Coz are revealed to be coaches at Factory. Their younger brother, Willy, is the player's final opponent in the Island Open.
A. Coz's name comes from the French term "à cause" which roughly means "because", the basis for B. Coz's name.