November 30, 2012 01:00 PM

Jason Merritt/Getty

The mystery has been solved: The reason behind Fred Savage‘s decision to not divulge details surrounding his new son‘s name is because … well, he doesn’t have one!

But leaving the hospital sans a moniker has become a tradition for the director and his wife Jennifer, who are also parents to Oliver Philip, 6, and Lily Aerin, 4½.

“We started this really tough precedent for ourselves where we just seem to leave the hospital with no name, and kind of live with the baby for a little while,” the former Wonder Years star told PEOPLE during Details 2012 Hollywood Mavericks event in Los Angeles on Thursday.

However, with a Friday deadline, the couple are under a serious time crunch. “The paperwork is due at the hospital tomorrow afternoon, so we gotta figure it out,” Savage shares.

“But we’re narrowing it down. We’re working on it — just as you are! We have some names in mind, but we kind of let the baby tell us a little bit.”

While the proud parents are caught up in the name game, Oliver and Lily have happily stepped into their new roles as big brother and sister.

“You’re always worried about how your kids will respond to a new baby, but they’re super excited and love holding him and being with him,” Savage says of the “awesome” sibling bond.

And with a new baby in the house, the family of five is looking forward to the upcoming holidays. “We do a lot of baking,” he shares.

— Anya Leon

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