It isn't often that fans get to see crossovers in which popular DC and Marvel characters meet face to face, but during the run of DC's Elseworlds books in the 90's, John Byrne brought us Batman & Captain America (1996). As both writer and artist, he gave readers a Golden Age style book in which the two iconic heroes teamed up to battle two of their equally iconic foes. With the nature of their team up, it only made sense that their secret identities would not remain secret for long.
Taking place during 1945 in the midst of an all out war against the Nazis, the 3rd Reich had infiltrated U.S. soil, and Captain America was called back stateside to face the threat head on. Coincidentally, where he was needed was no other than Batman's home turf, Gotham City. Captain America and Batman seemed to work well together to start, but unfortunately, Rogers' first direct order was to act as Bruce Wayne's personal guard, but not out of goodwill. Wayne was under suspicion of working with the Joker, and Rogers was sent to discern the truth.
In sleuthing, Rogers overheard the wrong part of a conversation between Bruce Wayne and Dick Grayson, thus creating a huge misunderstanding which led him to believe Wayne actually was in cahoots with Joker. So, when it came time for Rogers to confront Wayne, by dramatically breaking through a window, the two began to battle it out, mano a mano, with neither seeming to be able to land a blow on their opponent. That's when the realization happened. John Byrne's writing playfully allowed readers to hear both characters' inner thoughts as they fought, watching as they slowly pieced together who they were really dealing with due to each other's cunning and fighting prowess. Once they figured it out, they greeted each other as allies and went on to partner up and stop a Joker-Red Skull team up from blowing up Washington, D.C.
But this was far from the first time another hero deduced Batman's true identity. It's happened quite a few times, almost to the point in which it's surprising it still remains a secret at all. Some notable members of the not-so-exclusive "I know who Batman really is" club are the Green Lantern, Superman, the Green Arrow, and even Sherlock Holmes.
Superman is probably the most obvious one considering the man has x-ray vision and can just look straight through Batman's cowl to see the man under the mask. There have been a couple other occasions in which the two have figured out each other's secret identities as well, but the x-ray vision just makes it so simple that it's easily the most notable. As for Green Lantern, Batman revealed his secret identity as a sort of hail Mary when Hal Jordan was losing his mind in Justice League Vol. 2 #5 (2012). Really the only reason Green Arrow found out is because in Injustice: Gods Among Us (2013-2016), Huntress let Batman's real name slip and it really left him with no choice but to confirm it, leaving Oliver Queen visually gobsmacked. Sherlock Holmes is one that kind of comes out of left field, but it makes sense. When arguably the most famous detective of all fiction crosses paths with the best detective of all heroes, it was pretty much bound to happen.
Of course, this group only includes a handful of characters who have discovered the Batman's secret identity. The complete list is a lot more comprehensive. It really begs the question of how he ever gets away with maintaining his anonymity in the first place. One thing is for sure, though, Batman is lucky Elseworlds: Batman & Captain America takes place in a universe outside of the normal DC and Marvel canons, otherwise he'd have one more person to worry about when it comes to blabbing his identity to the world.