Most likely no......
Children usually get their father's name and since Sparda was a demon its a strong possibility demons don't have last names so either Dante and Vergil has no last names or inherit their mother's last name.
We can always use their mom's maiden last name but we'll never known because Capcom (even Kamiya) has to be careful otherwise any last name they could've given Eva probably will probably be used on them and Dante and Vergil have names that really suit them, they must have a last name that screams badass (Jack Caymen, Henry Touchdown, Marcus Fenix) but believable but I doubt you gave them a last name that is badass and believable as a last name for Eva and it could be difficult.
What Im saying is coming up with a last name for Dante and Vergil would be hard.