In fact, at one point, he was gunning for a name that showed off his loyalty to his favorite college football team, the Iowa Hawkeyes.
"There was a rallying cry from a collective that believed in the name Hawkeye," he said during an appearance on "Conan" on Nov. 16. "I'm an Iowan, so to have a kid named Hawkeye?"
"It's like M.A.S.H. -- like, he could be a doctor!" Ashton continued, referring to Benjamin "Hawkeye" Pierce on the TV series.
His college-centric contribution to the name game "didn't fly" for very long, though, he reluctantly admitted.
"It didn't get across the Mila threshold," Ashton said. "It came to the threshold, but then it got knocked down."
Their baby boy won't go nameless, though.
"We have a name dialed in that we've had for a while," the actor said. "But the problem is, if you get the name too soon, suddenly there's like slight trepidation about the name. The other day, Mila was like, 'So, you still like the name?' And I was like, 'Yeah.' And she was like, 'Why was it the high-pitch yeah? Why wasn't it the low-pitch yeah?' Then I was like, 'Well, you like the name, right?' She was like, 'Yeah.' Like, 'Why did you say it like that?'"
The sudden uncertainly made the couple wonder about the namesake of their child.
"Now we're like, 'Maybe we don't love the name,' even though we both love the name!" he said with a laugh. "So, I think we have a name."
The couple already share a 2-year-old daughter, Wyatt, so they've been through the drill before. However, he's quick to point out that everybody's past comes into play when you're naming a child.
"You don't want names of people that remind you of people who used to beat you up," he explained. "That's not good."