The name Azure is a girl's name of French origin. Azure and is often added to lists like Color Names for Babies and discussed in our forums with posts like "Names on NB that make you go WOW!".
From the experts:
Azure is a colorful choice for a blue-eyed child. Among other blue-toned color name possibilities: Indigo, Cerulean, and Blue itself.
In the Middle Ages, azure was another name for lapis lazuli, the gemstone used to make the brilliant pigment seen in much medieval art.