It's just Bane. He doesn't have a real name. He was raised, in prison, going by the name Bane. It's the name he had as a child. It's the only name he's ever used. It's the only name he's ever needed.
Additionaly- Banes Family name was Dorrance in Santa Prisca, the fictional homeland from the comics. His father Edmund (or Edward?) Dorrance a revolutionary that eascaped and so toddler Bane was sentenced to serve in his stead. He is a brilliant and ruthless criminal genius that even Ras Al Ghul respects. The above writer is quite correct in that Bane never refers to himself as anything but Bane. His teddy bear was Osito, it concealed his shiv.