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Everyone who believes in Batman knows who he is. A detective with a strong sense of justice who never seems to take a break, stoic and no nonsense but has a softer side? That’s commissioner Gordon alright. Good with victims? Check. Terrifying for criminals? Check. Experienced? Check.
Everyone knows how corrupt the police force is, would it surprise anyone if Gordon worked outside the law too? It's hardly unusual for a Gothom cop. At least he is trying to do good when he takes things into his own hands. He probably came to the same conclusion as so many gothamites before him, the system isn’t working. He's easily clever enough to keep such a secret. I
Everyone knows Batman is commissioner Gordon. Who else would he be, Bruce Wayne? Don’t be silly.
Why else would Gordon be the only police officer to “communicate” with the Batman? And always at the police station. Always on the roof when Gordon takes a 'smoke break'. Despite their supposed collaboration they’ve never been seen together. Batman always disappears before Gordon arrives. He never leaves notes for the police, like he’s afraid they’ll recognise his handwriting!
Why else would Gordon require so much caffeine to function, it helps him stay awake when working around the clock. And how else would Batman be able to refer people to the best jobs all the time? Obviously the police commissioner would know which homes and schools and businesses are good and law abiding. Clearly the commissioner has contacts there from inspections. That's how Batman gets criminals jobs and street kids homes.
It’s obvious, Batman is commissioner Gordon. Everyone knows it, including Superman.