The Golden Age
Floyd Ventris is a criminal scientist who uses mirrors in his crimes, in a fashion similar to Mirror Master. In both his meetings with Batman, Ventris tries to expose Batman's secret identity.
The Modern Age
In the modern age there is reference to another Mirror Man. Nothing is really known about the past of this Mirror Man. When he arrived at Arkham Asylum, he did not even have a name. He is obsessed with looking at his reflection in mirrors and talks to himself in a language that no one understands or repeats what others have already said. He was given the name Narcissus by Dr. Jeremiah Arkham.
Five years prior to arriving at Arkham, he walked naked out of a forest in Haiti.
It turns out he is merely a figment of Jeremiah Arkham's imagination.