Horror movies usually are titled after the monster. Dracula. The Mummy. Alien. Jaws (for the shark).
Hitchcock followed along with that tradition in Psycho. Who's the bad guy monster? Well, the title tells you: it's the psycho.
But hold on a second. Who is the psycho in question here? For most of the film, if you're watching for the first time, the psycho looks like it's Norman's mother, Mrs. Bates. It's only at the end that you learn that Mrs. Bates is "as harmless as one of those stuffed birds"—since she's dead, like the birds. The real psycho, the one to watch out for, is Norman.
But hold on another second. At the end of the film, the psychiatrist dude says that Norman isn't "Norman" anymore, but has been taken over by his mother. The final voiceover is Norman thinking with his mother's voice:
"He was always bad, and in the end he intended to tell them I killed those girls and that man..."
Norman dressed up as his mother, and killed because he thought his mother would be jealous or upset. But then—as his mother—he says that it was Norman all along. Is the psycho mother? Norman? Both? Neither?
Psycho, then, doesn't refer to one person or the other. The monster in Psycho isn't a monster with big teeth and a distinct identity. It's the loss of identity. Psycho could refer to Mrs. Bates, or it could refer to Norman. But it could also refer to the state in which you can't tell one from the other.