And I think it's intentional as it refers to Doppio being an unnatural being. I know it means double vinegar, but no one uses Aceto as first name and Doppio as last name in Italy. I too am Italian like you.
Doppio's full name "Vinegar Doppio" basically means a Double Shot of sour tasting Espresso. "Doppio" is a double shot espresso after all while the "Vinegar" is a sour-tasting liquid.
And I know that no one uses Doppio as last name, but it's not like a italian priest would name his child "Diavolo".
Doppio simply has a surname. Diavolo is also more unnatural than Doppio. While Doppio shows signs of Dissociative Identity Disorder, Diavolo is unnatural and demonic. No surname, named after the devil, the only one who could latch onto another person's soul when Silver Chariot Requiem swapped everyone's souls.
No, it was just said that the son's name was Diavolo in the manga which is already weird enough cuz why would a italian priest name a apparently "open-hearted and cowardly" boy (Which sounds like Doppio) after the devil? Part 5 has a lot of religious symbolism, I wouldn't be surprised if Doppio was possessed by the literal devil, it'd explain the long pregnancy of the mother. "Dio" means God after all, so Giorno is God's son, fighting the devil, Diavolo, the Antichrist who possessed Doppio.