From Online Etymology Dictionary:
Capri:
island in the Bay of Naples, of unknown origin: L. capra "she-goat," Gk. kapros "boar," Etruscan capra "burial place" all have been suggested.
I think of goats, myself. Sorry. I kind of like the possible nicknames based on the stressed syllable, though (Pri, Prina). Otherwise, why not just
Catrina. People probably mishear it as
Catrina often.