There's a moment, either in a Justice League comic or maybe in one of the cartoons (I unfortunately don't remember), where Wonder Woman holds out her Lasso of Truth and has Superman and Batman hold it as well so they can all introduce themselves

"I'm Diana," she says
"Clark Kent," says Superman
"Batman"

It's such a good joke but also like

Yeah, that's who he is

Bruce Wayne is Batman's alter ego, not the other way around