Latin's tradition in appellation differs from that of the Romance languages. "I call myself," is the modern pattern, or "I am called.". But Latin had a 'dative of possession,' which was very handy; meaning that a Roman would say, "the name to me is Luke," for example. It seems frightfully awkward in English, now that I write it out, but it just feels like second nature in Latin.
The dative of possesssion is not unknown to Romance languages, though it is not used in connection with names. Compare French:
Ces gants ne sont pas à moi - 'These gloves are not to me' = These gloves are not mine.
Cette montre est à elle = 'This watch is to her' = This watch is hers.
This construction has similarities with:
Nomen ei est Marcus - The name to him is M. = His name is M..
Come to think of it, is the possessive dative only used with names in Latin or can it be used in the French way too?