I still don't get how you assume Joker finds out Bruce is Batman after realizing its not Dent?
That's quite a stretch. Joker only found out its not Dent but that whoever is Batman cares for Rachel too.
Thought it was Dent because he cared for Rachel, knew if he went after Rachel it was someone who cares for her, after Dent it might be well publicised childhood friend Bruce Wayne.