If you are talking about English stone names, think they're good and somewhat unique (but not all of them). My favorites are
Topaz, Peridot,
Diamond, Sphene, and
Amethyst. Aside of them, there are also
Jade,
Emerald,
Amber,
Sapphire,
Goldie, Tourmaline, Aquamarine,
Ruby, Carnelian,
Beryl,
Garnet,
Opal, Catseye, Calcite,
Pearl,
Rocky, Lapis Lazuli, etc.
But won't you name your character/child any names like
Stone, Fossil, or anything like that, right?