Dative of Possession
Isn't it the genitive case that shows possession? Well, yes, but the dative can also under certain conditions, the principal one being that the main verb of the sentence is a form of the verb “to be.” The “dative of possession” is actually more of a “dative of reference.”
Nomen illī mulierī Tanaquil erat. With reference to that woman, the name was Tanaquil. As for that woman, the name was Tanaquil.)
It's just easier to say:
That woman's name was Tanaquil.
Body parts and other personal effects often use the dative of possession instead of a genitive. For example: Dominus caput servī percussit literally means “The master hit the head with reference to the slave” meaning “The master hit the slave on the head.” Obviously this was to the slave's disadvantage, so a dative works best in this sentence.