What can it mean that he calls me "bro"?

He can’t be bothered to remember your first name.

Just a casual term of endearment, that’s it, no need to circumnavigate his reasoning.

Assume for the sake of argument that he likes you back. If so, he is just as nervous talking to you as you are talking to him. He might even be more nervous given the expectations put on men in these situations (they’re supposed to “make the first move,” essentially taking all of the social risk). He will feel the need to play it cool while also trying to get you to like him.

It’s a difficult calculation, and even more difficult if he is younger (due to the lack of experience and the overload of hormones). And for all we know, he’s at home right now asking himself, “Should I not call her bro? Is that getting the wrong message across?” I agree with @ucme that you should cut him a break. Most likely, it’s just part of this guy’s natural vocabulary that slipped out while talking to you.

I would not worry about what he calls you, as long as he calls you.

My theory is that because the guy is supposed to take the social risk he will be more attractive if he comes across as social proof and cool. By calling you bro / dude he could be trying to show you that he doesn’t give a care if you accept or reject him because you are just another person to him and not someone he is going to drool over.

If I were you, I’d say, “Dude, why do you call me bro? I have a name.”

Sounds like a habit he’s not even aware that he’s doing. “Bro,” is a term used to refer to other men who are friends.

Are you male? Maybe he thinks you’re male. Otherwise, I have to say that is seriously messed up. It sounds like hipster language gone seriously awry.