Yes, Anaxandra is a real name. Some pronounce it ann-ax-ANN-druh, while others say ann-uh-ZAN-druh. This Greek female name is a great example of an ancient woman who was very accomplished. Anaxandra was the daughter of Nealkes, who painted mythological scenes in ancient Greece, and she was also his student. She lived around 228 B.C. and was mentioned by Clement of Alexandria (2nd century) in his work Women as Well as Men Capable of Perfection. She was also important enough that the International Astronomical Union named a crater of Venus after her.
This is also a literary name, used by Caroline B Cooney in her novel Goddess of Yesterday.
There are no girls in the U.S. given the name Anaxandra.