Arpad Busson and Uma Thurman
04/22/2014 at 06:00 PM EDT
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