The 'Bel Ami' actress, who gave birth to her third child on July 15, would like to call her Luna rather than her staggering five names, reported People magazine.
"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. Each name has a special reason and meaning to her mother and father," the actress's representative Gabrielle Kachman said.
The baby is the first child for the 42-year-old actress and Arpad Busson, 49, but the 'Kill Bill' star is already a mother to daughter Maya, 14, and son Levon, 10, from her previous marriage to Ethan Hawke.
The couple have been dating since 2007 and had a brief split in 2009 before rekindling their romance.
Thurman will be seen next in NBC musical TV show 'Smash' and with Robert Pattinson in 'Bel Ami'. She will also be starring in sports comedy drama 'Playing for Keeps' along with Jessica Biel, Catherine Zeta-Jones, Gerard Butler and Dennis Quaid.