A second self.
The uses of this phrase, which derives from the Latin 'other I', range from psychoanalysis to films and popular fiction. The term is also the name of a popular computer game. Recently it has been much used in stories of superheroes like Superman and Batman, who require a day-to-day human guise. Before that we had Dr. Jekyll and Mr. Hyde.
The concept of an alter ego, that is, a second self, was put forward by Cicero as a philosophical construct in 1st century BC Rome.
The term is first recorded in English in 1537, in a letter written by Richard Layton to Thomas Cromwell, regarding the suppression of the monasteries:
"Ye muste have suche as ye may trust evyn as well as your owne self, wiche muste be unto yowe as alter ego."