07/18/2011 at 11:00 AM EDT
Why announce a name yourself when your famous father can do it for you?
After delivering a daughter
Sunday morning, Ivanka Trump is resting up – while Donald Trump shares some happy news.
"I just left the hospital and the baby is beautiful. [Ivanka's] doing great," Trump, 65, tells Fox & Friends
. "Arabella Rose is the baby's name – I just found that out by the way."
Shortly thereafter, Ivanka announced the name herself via Twitter
"Jared and I are having so much fun playing with our daughter!" Trump, 29, writes. "Arabella Rose is beyond adorable. She's truly a blessing."
This is the first child for Ivanka and the third grandchild for Donald Trump. Son Donald Trump Jr. is already dad to daughter Kai Madison, 4, and son Donnie III, 2, with another boy on the way