The 42-year-old has given her daughter a long name but will be known an Luna to family and friends. The actress gave birth to her July 15.
"I would like to announce Uma and Arki's daughter's name for the first time officially: Rosalind Arusha Arkadina Altalune Florence Thurman-Busson, better known to family and friends as Luna," thesun.co.uk quoted Thurman's spokesperson as saying.
This is Thurman's first baby whereas Busson's third child. He has two children Maya, 14, and son Levon, 10 with ex wife Ethan Hawke.