Her daughter, born in July is Rosalind Arusha Arkadina Altalune Florence Thurman-Busson. But a spokesman says family and friends call her Luna.
Thurman, 42, kept the name a secret until now. She says every part of the name has special meaning.
Luna is Thurman's third child, the first with boyfriend Arpad Busson, 49. Thurman has two children with ex-husband Ethan Hawke.