Canonically, I think his default name is "Jack." Waaay back in 2003, I sent Nintendo of America a (then) massive character wishlist of like a 60 character cast for Smash and my three third party picks were him, Geno, and Megaman.
Actually, Jack is a fan name that became so pervasive that it's often mistaken for the real thing. Per a couple of games, his actual default name is Pete. No one really uses it, though.
Not to mention that if we did get the Farmer, his name probably wouldn't be Pete given that the
Bokujō Monogatari series is localized by Xseed Games under the brand of
Story of Seasons now, while Natsume did localization in the past under the
Harvest Moon title (Natsume now develops their own games using the Harvest Moon title, adding to the confusion). In the first game under the
Story of Seasons name, there were a couple of returning characters, and XSeed's localization team decided against Natsume's old localized names for them, so the same would likely apply to Pete. So who knows, maybe if we ever did see the original farmer again, Xseed would go ahead and make the fan name official.
Jack/Pete was actually one of my preferred newcomer choices back in the Brawl days, as I rather enjoyed the series. Don't really actively support nowadays, especially since the Villager kind of filled a similar role, but I would still be down to see him.