In this context, the first baseman is named "Who"; thus, the utterance "Who's on first" is ambiguous between the question ("which person is the first baseman?") and the answer ("Who is the name of the first baseman.").
Abott:What is the guy's name on second base
Costello: Im not asking you Who's on second!
Abott: Who's on first!
Costello: I dont know!
Abott: He's on third, we are not talking about him."
"That Who's on first? Routine always makes me lol"