From the experts:
As flower names become more exotic, so can gem names move beyond Ruby and Pearl to names like Topaz, Sapphire and Peridot. Amethyst, the purple birthstone for February, has never been in the Top 1000, but could have some appeal, joining similarly-hued Violet and Lilac, all of which make great names for Aquarius babies or names for February babies.
In the M.M. Kaye children's novel The Ordinary Princess, the protagonist is Princess Amethyst Alexandra Augusta Araminta Adelaide Aurelia Anne of Phantasmorani --Amy for short --who has been given the "gift" of ordinariness.