Arpad Busson and Uma Thurman
and financier Arpad Busson have ended their engagement
The couple decided to call off the wedding months ago, PEOPLE has confirmed.
The pair began dating in 2007 after attending a private dinner together in Milan. They got engaged in 2008 and have a daughter together
, 21-month-old Rosalind Arusha Arkadina Altalune Florence.
Thurman, 43, revealed why their little girl has so many names
. "We couldn't quite agree on the name," she told Jimmy Fallon. "We call her Luna, so she's lucky that way."
Thurman has two other children – daughter Maya, 15, and son Levon, 12 – with ex-husband Ethan Hawke
. Busson has two sons – Flynn, 16, and Cy, 11 – with supermodel Elle Macpherson
Reporting by JULIE JORDAN