Batman being Bruce Wayne can actually work when you think about, first off it's always implied that people just didn't believe Batman was a thing in early stories and is just a legend since he always used stealth and hiding, add that with the psyche of criminals, no thug would actually admit that he got his ass handed to him against a single dude, especially when you were ganging on him with 8 guys, you'd be humilliated. By the time he's already revealed to be a thing Superman, Wonder Woman and Aquaman are there too, if aliens, Greek Gods and Atlanteans exist, they'd think Batman is just a supernatural vampire guy, Batman would be smart enough to park the Batmobile somewhere hidden so people don't find out about his expensive gadgets and shit, even then Bruce Wayne would be obsecure outside of Gotham, how many of you know who Mark Cuban is?