I googled exact phrase "Who is captain" and most results seem to be "Who is captain Jack Sparrow/Phasma/America/etc.", therefore questions about specific characters. Or questions like "Who is Captain America fighting with?" So I think it really should be "the captain" here.
By the way, if you really were to ask something more about Captain Jack Sparrow (because maybe you've never heard of him), it would be "Kim jest kapitan Jack Sparrow?"
Thank you :) My question was more about the different between "Who is the captain?" and "Who is captain?", just like you enter a room and you're just looking for a captain, but no one in particular, like in "Is there a captain here?" I'll ask someone bilingual i know and i keep you posted.
If you for some reason mean 'a captain' (although that seems kinda strange to me, as if it's not exactly a profession, like a doctor or policeman), whether it's captain of a school football team or a captain in the Army, the Polish sentence wouldn't change anyway. Although "Is there a captain here" would make more sense in my opinion indeed, and that would be "Czy jest tu (jakiś = any) kapitan?" :)