But Na -- the Seattle Mariners' director of baseball administration -- never really gave the name more than a passing thought at the time.
"It started with just Cooper ... because we were in Cooperstown," Na said Tuesday. "The thought of doing it, at first, was kind of silly. We joked about it at first. It took a little bit of convincing on my wife's part."
Apparently, Cory Na decided to get on board with the idea, and on Jan. 18, she gave birth to a baby boy named Cooperstown at Swedish Medical Center, much to the delight of, oddly enough, Mariners general manager Bill Bavasi, who had been an advocate of the name since the idea was first hatched.
"Bill was originally the one who started the ball rolling," Na said of the push to name the Na's first-born Cooperstown. "We exchanged voicemails during her 14-hour labor."
Brad Horn, the communications director for the Baseball Hall of Fame, said that he does not know of any children named Cooperstown.
"As far as we can tell, Cooperstown has his own place in history as the first," Horn said. "Hopefully, he'll enjoy a lifetime of baseball memories, and will come to love the village of Cooperstown in the same way that so many and fans of the game have done over the years."
Na realizes his son won't likely go by his full name. "Someone is going to call him that maybe, but most will call him Coop or C.C. or C-Town."
Cooperstown's middle name is Charles.
"They're doing outstanding," Na said. "Mom is at home and healthy. The baby is getting big. He had his first doctor's appointment [Tuesday]."
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.