I can say that Nygma discusses his villainous past openly, just as much as he does his reformation. He's an odd one, though. Something about him never quite clicked favorably with me. [ mostly that for years he harbored a dude who betrayed and killed her once and never had the good sense to stay dead. it's complicated ancient history. ]

I can't say much of anything about Cobblepot, I've never actually spoken to the man. And I can't say much of anything nice about Dent.

[ again, would totally break that dude's legs and not even feel guilty about it. but the motivation to is lessened with renee gone. ]

I suppose it shouldn't surprise me that either of the three has an infamous reputation in their home universe.