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Also why does Bane in particular is the one who figures out batman's identity from public knowledge? I understand that's also how Doctor strange found out but Strange is an incredibly intelligent psychiatrist with tons of experience in behavioral analysis.
what are Bane's qualification for coming to this conclusion?
It's unearned imo, and I think this feat should've been given to a more intelligent villain like The Riddler.
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That's the thing, though: Bane is in fact incredibly intelligent and clever. His whole deal is that he's not only the physical equal of Batman, but also every bit the mental equal as well. He also makes elaborate plans, just like Batman! In fact, in his very first appearance, he deduces Batman's identity from news reports and other clues and concocts such a plan that leaves Batman battered and exhausted, and Bane suddenly appears, reveals that he was behind everything, and then breaks Batman's back!
This aspect of Bane is pretty badly represented in most of his non-comics appearances, where he usually gets presented as just another super strong villain. But it's a fundamental and core part of his character; Bane's appearance in Origins is far more interesting and better written then when he shows up in the other Arkham games, where he's just a big hulk of muscle for Batman to fight.