The Grease star then sung his original ditty for reporters: "Benjamin Hunter, that's my name! Benjamin Hunter, that's my name! Benjamin Hunter. Ba ba bum. Ba ba bum!"
To attend Saturday's event, Travolta and Preston, 48, left their little guy at home with his big sister Ella Blue, 10, and a babysitter. "I called home three times in the last hour and he’s doing well," the actress said Saturday. "He's perfect! He's fine."
"Ella loves Benjamin," Travolta noted of their daughter. "She just can't stop loving him."
The proud mom added that Benjamin takes after his dad in the looks department. "Identical!" she said. "Maybe there's me somewhere in there, but he looks so much like his daddy," she gushed of her "dreamy" new son.
The biggest surprise about parenthood this time around? "Our age!" Travolta quipped with a laugh. "To start...it's a miracle."
Indeed, the famous couple conceived their child about a year and a half after the tragic seizure-related death of their son Jett, 16. "He's brought us a new beginning," the duo told HELLO! magazine. "He is the best gift we could possibly have."