When I see a Japanese translation of Vergil it usually comes out in the translator to English as "Virgil", probably because the auto translate is assuming reference to Publius Vergilius Maro's moniker "Virgil" in English texts. I see more English spelling of Virgil than Vergil on Japanese and Chinese sites and this might be why.
Virgil is a bastardisation of Vergilius, but is more well-known than 'Vergil' when Virgil's poetry was widely translated into English books, so Virgil is now assumed the 'correct' spelling when referring to Virgil himself. In DMC terms, it has and always will be Vergil - when a fictional character is presented with a particular spelling of a name, and as long as it doesn't change between presentations - I wouldn't refer to them by some more commonly-used spelling, because it simply isn't their name. Their name is what we were given by the creators, even if it was a mistake (like Nelo Angelo)