Latinized form of Greek Ναρκισσος (Narkissos), possibly derived from ναρκη (narke) meaning "sleep, numbness". Narkissos was a beautiful youth in Greek mythology who stared at his own reflection for so long that he eventually died and was turned into the narcissus flower.
This name appears briefly in the epistles in the New Testament and was also borne by a few early saints, including a 2nd-century patriarch of Jerusalem. It has been used to the present, especially in Catholic regions, usually in honour of the saint as opposed to the mythological character.