Parker and Broderick Name Baby James

The couple’s baby boy is named for his dad’s late father.

Sarah Jessica Parker and actor-hubby Matthew Broderick have named their newborn son James Wilke Broderick, in memory of Broderick’s late father, actor James Broderick, their publicist confirmed Friday.

The boy was born early Monday morning at Lenox Hill Hospital in Manhattan, weighing in at 6 lbs. 8 oz. Parker’s publicist confirmed at the time that “mother and baby are doing very well. Everyone is healthy.” Broderick’s rep on Friday told the Associated Press that “everybody is totally over the moon and ready to go home.”

The family did just that Friday afternoon. Broderick and Parker left the hospital and gave photographers a carefully orchestrated first glimpse of their new son before heading home.

With the baby sleeping, the family posed for about 100 photographers and fans waiting outside the hospital.

“Thanks for caring,” Parker said, according to the AP. “It must be a slow news week.”

Meanwhile, the news of the name formally shoots down the New York Post’s report earlier in the week that the couple had opted for the name David Perkins Broderick. (The paper said the name was on a placard posted outside the actress’s hospital room.)

The baby’s namesake, Matthew Broderick’s father, James, starred in the 1970s TV series “Family” as well as films such as “Dog Day Afternoon” and “Alice’s Restaurant.” He died in the early 1980s.

This is the first child for Broderick, 40, and Parker, 37, who had talked about having kids ever since their marriage in 1997. The pregnancy news came soon after Broderick wrapped his run on Broadway in “The Producers.”

• For more on the baby and the happy couple, check out this week’s PEOPLE cover story.