Whether he's Villain or Vigilante, the Joker knows Bruce Wayne is Batman. What would the Joker do with this information in season 3? Would he try to blackmail Bruce with the knowledge, or keep it to himself?
Joker wants that knowledge all to himself. That’s why he didn’t tell Harley. If he told anyone it wouldn’t be between them anymore and that would kind of ruin it for Joker. He treasures their little secret.
He'll treasure it always. He's not the blackmail sort. It's more fun to have that over Batman's head, and maybe drop by his house unexpected sometime. Joker's not good at sharing with others.
As everyone already said, nothing. It's personal, he won't share or use it as a blackmail.
Nothing, he wants Bruce/Batman all to himself