Donald Trump Jr. and his wife Vanessa.
Brian Prahl/Splash News
05/13/2007 AT 12:05 PM EDT
Donald Trump has a new name to answer to: Grandpa.
Son Donald Trump Jr. and wife Vanessa, both 29, welcomed their first child Saturday afternoon in New York City, the couple told PEOPLE.
The 6-lb. 14-oz. girl, named Kai Madison, joins uncle Barron
, The Donald's own 1-year-old son with wife Melania, among the youngest Trumps.
"Everyone's great," Trump Jr. said in a phone call from the hospital. "Baby's great, Vanessa's great – and I'm getting used to the idea [of being a father]."
And what's the origin of the baby girl's unusual name? "Her [maternal] grandfather," he says. "It's Danish. He's a Danish musician and we wanted to keep it as a family name."
It was a "hectic" day at the hospital – Kai was not due for another two weeks – but the new dad, an executive in the Trump Organization, admitted the birth "is definitely a changing experience. It's very cool."
When the couple first announced the pregnancy in November, Vanessa told PEOPLE
, "Everyone's very excited," although "if you mention the 'grandpa' word [to Donald Sr.], he might not be so excited."
Kai just might change that.