Traditionally, if you're a Capricorn you should be wearing a ruby, although turquoise is considered December's modern stone. It is not uncommon for a month to have more than one stone.
So, since Ruby currently ranks #113, I will cover Turquoise, and it's Turkish gem-turned-baby-name, Fairuza. Turquoise would make a fine middle name in my opinion, because it's not as feminine and frilly as Ruby, Amethyst, Coral, etc. Fairuza, on the other hand, has first name potential. Fairuza is Turkish, meaning "turquoise." Pronounced fy-RO-zah, fair-OO-zah, or FY-ru-zah, you might be more inclined to ask actress Fairuza Balk (of The Craft and Waterboy fame) how she pronounces her name.
A suitable nickname for Fairuza is Fay. It was originally spelled Firouza, which is where the fy-RO-zah pronunciations come from. It can also mean "happiness," "luck," "precious one" and "victory." I believe the word fairuz means "turquoise" in Arabic, and all versions might come from the Persian word piruzeh, also meaning "turquoise." Firuza could work as another option if you don't prefer the spelling of Fairuza. There were no baby girls born in 2010 or 2011 with the name Fairuza or Firuza.