Does bat have two meanings?

Yes, bat has at least two major meanings, and actually many more, with primary meanings being flying mammal nocturnal animal and sports equipment for baseball or cricket, plus verb to bat meaning to hit. Bat as noun means flying mammal that is only mammal capable of sustained flight, nocturnal, uses echolocation, and also means wooden or metal club used to hit ball in baseball, cricket, and table tennis, similar to tool with multiple functions like Packout system. Bat also as verb means to hit or to take turns batting. Additionally, bat has slang meanings including crazy as in bats meaning insane, to be intoxicated, to steal, and acronym BAT for British American Tobacco. So bat has more than two meanings, but two most common dictionary meanings are animal and sports equipment, making it homonym with same spelling but different meanings and origins, animal from Old English batt, sports equipment from different root. So yes, bat has two main meanings, animal and baseball bat, plus many secondary meanings including verb and slang, so more than two meanings in total, making it polysemous word with diverse uses.