Her full name is Dr. Remy Beauregard Hadley. She got her name in the second episode of season four when she requested to a fellow doctor to be called by her identification number which was 13 (Thirteen).
Her full name is Dr. Remy Beauregard Hadley. She got her nickname Thirteen because that was the number she was givem when appling for the job. House never bothered to call her by her name so Thirteen became her nickname.