According to IMDB
Selina leads Batman to Bane and sticks around long enough to hear Bane call Batman his real name, shocking both Bruce and Selina. John Blake discovered as a child when Bruce came for a charity donation to the orphanage Blake resided in. Upon seeing Bruce, Blake worked out he had severe suppressed emotions that would give him a motive to become The Batman who appeared years later. He challenges Bruce with his suspicions of his alter ego when visiting. Though Bruce does not confirm his theory, he doesn't deny it either giving Blake the evidence that Bruce really is The Batman. James Gordon is the only character directly told by Bruce Wayne (as Batman) that Batman is his alter ego. Batman reveals his identity by referencing the act of kindness Gordon showed him as a boy by putting a coat around his shoulders after his parents' death. Gordon remembers the incident with the child and puts two and two together, working out Bruce is The Batman.
Selina Kyle learns Batman's true identity from Bane, who calls Batman by his real name. But how did Bane know Bruce is the Batman?