We don't see this until the ship runs aground at the mer-people's breeding ground, but her name, painted on a wooden plaque, is "Marie Celeste".
This film was shot in 18 days.
Ther mermaid's caudal fins make reference to ancient or medieval depictions of twin-tailed sirens, or melusines, which became subject of confusion with mermaids throughout history. Such figures inspired, for instance, the Starbucks logo, which is a siren/melusine.