I have no name for I am but 2 days old ;).
I'm not denying that Urizen is Vergil's demon half while is V is Vergil's human half, i just think its too simplistic. Especially in a series where there are good demons and bad humans.Urizen is vergil demonic half without his human half V, is vergil human half That restrain him from doing bad bad bad things, that s why vergil split himself so that he can do what he need to do whitout limit... In mission 17 if you look closely you can see that the location of the battle, the house of vergil family, its in reality an urizen memory, his last part of humanity that its still attached to him, Infact when he eat the fruit the location begin to fracture like a glass and dante say that his last part of humanity his now gone, during the battle the location continue too fracture multiple time, demonstrating that Infact urizen had some connection to his memory but that last part of memory is now gone by eating the fruit and he only care about power now...
A more specific approach is Urizen is the part of Vergil that still thinks power will solve everything while V is the part of Vergil that realizes seeking power at all costs hasn't really worked.
I don't think V is inherently good, he just made the choice to be better/different than he was before. There is also circumstances like his body falling apart that also pushed him into certain paths. You could even make the argument he still wants power as it comes up in a taunt as well as the end of mission 17. So the potential to fall back into old habits is still there.