A woman walking along the street by a large white building is suddenly stopped by a man who asks who she is and what she is doing there. She walks on, however, not knowing he was addressing her. She stops and thinks, realizing that she doesn't know who she is; she has no memory. She goes to the door of the white building — where she thinks the man lives — to hopefully find some answers.
A sign on the door directs her to check her pockets. She does so, and finds a note describing her condition. She was a criminal, and was offered one of two sentences: to be exiled to a prison planet, or to remain on Earth with a memory wipe and new identity. She had evidently chosen the later, and this building is the center for helping these "new" people get back into society, providing a living place and a new job. She gladly accepts her new life.
A very short story, "Identity" appeared as part of the 1978 Chattacon Convention's program booklet; van Vogt was the guest of honor at this event, and this story was a kind of bonus. It was published only once more, in an anthology, and has yet to appear in one of Van's collections, making this story very difficult to get hold of.