Yeah, as others have said, it's pretty common for Gordon to either avoid trying to figure out his identity or just outright pretend he didn't.
There's a bit in No Man's Land where he's pissed off Batman abandoned the city after everything went to hell, so Bruce tries to reveal his identity to show that he does trust Gordon:
https://gamefaqs.gamespot.com/a/forum/3/3ae5063e.jpg
And in TAS, there's an episode where Barbara has a fear toxin nightmare of him discovering she's Batgirl after she died, so she decides to tell him. Before she can say anything outright, he cuts her off by very strongly implying that he knows but can't acknowledge it Relevant bit is at 1:30. Sorry about the quality, cannot find another clip.
https://youtu.be/rfAvBpNOdsE?si=zdPZ2fBj822H1E-m&t=89
R_Jackal posted...
I feel like it's logically hard not to know there's a limited amount of people both invested in Gotham so heavily, and access to things like private fighter jets, high-end military gear, and experimental vehicles.\
I always just figured most people "know" but just can't or don't care to confirm.
There are other possible explanations though. In the Arkham games, Riddler thinks it's obvious that Batman steals money from the criminals he stops to fund his activities.
And Bruce isn't an idiot, he fucks with that idea too:
https://gamefaqs.gamespot.com/a/forum/a/a40e0ca3.jpg