Eye of Death puzzle

When Jack and Micki arrive at Rook's apartment after he had dumped the woman's body in the dumpster, they are met outside by police for questioning. Jack says his name is Atticus Rook which satisfies the detective who says he will need more information from them after a while. But when the detective goes to Rook's apartment later on, Rook answers the door and the detective asks his name, etc. He obviously does not look like Jack, so the only thing I can figure is that either the detective was too busy with the case to catch that his appearance has changed or it was a different detective. Did I miss something?