What was Ariels mothers name?

Her name is Athena, according to the DVD-only movie "The Little Mermaid: Ariel's Beginning" (released after "The Little Mermaid II: Return to the Sea," but because it takes place before the events of the first "The Little Mermaid," it's a prequel).

She died when pirates spotted the merpeople lounging at a lagoon; the presence of the ship and their plundering scared most of the merpeople off, but Athena stayed above in order to try and recover a music box Triton had given to her. She was (supposedly) pinned in between the rock where the music box lay and the ship, and the ship crashed into her, crushing her.