Okay, yes, the name “Gardner” is technically not spelled the same as the word gardener. On the other hand, it seems incredibly likely that it etymologically evolved from it. That means it probably is one of several surnames that are derived from some sort of profession. By most historical accounts, names of the likes of Baker, Carpenter, Butcher, and others originated in England. People who have one of those last name probably have ancestors hundreds of years back that worked the profession whose name they now bear.
Therefore, we might be able to infer that Brett Gardner had an ancestor who might’ve been a gardener.