And where is the Batman? HE'S AT HOME WASHING HIS TIGHTS!
Only villains will call him The Batman. It's derisive or disrespectful in some way. By not using The, you acknowledge he is the only one. The means he could be one of several Batmans (Batmen?) i.e. This Batman vs. That Batman. Although really, it would be very safe to assume that there is only one reclusive billionaire genius who dresses up as an anthropomorphic bat and terrorizes criminals by night. Not too much competition in that category.