It seems that he doesn't know but if we analize some dialogue in the game dante probably know but doesn't reveal this to V or anyone else and just kept it for himself, but the motivation is unknown
When dante first meet griffon, shadow and nightmare in mission 18, griffon reveal to Dante that they are vergil nightmare when he was nelo Angelo and griffon say this exact world to Dante after the revelation: but you knew that already
And dante replay whit this world: come to think of it, I did know something was off...
So dante probably knew that V was a part of vergil, and his familiar were vergil nightmare
Also v is taking whit him the William Blake book when he visited dante at his office, this book can be seen in a flashback in the manga vision of V, in this flashback we saw kid dante and vergil playing tougheter and vergil is reading that exact same book... So dante saw vergil in possession of the book, but didn't react when seeing it in V s hand, why? did he completely forget about that book, or he knew the truth but kept it for himself
Also in mission 12 when dante reach his old home he says that Yamato can separate the man from the devil, but how did he know this? Probably because he knew that vergil used the Yamato to separate himself into two part, V and urizen...
Also at the beginning of mission 18 after vergil disappear in the portal, Nero ask himself what the hell happened to v and dante respond by saying that he returned to himself... So During this cutscene dante came to the conclusion that V is vergil human side, but Nero who should have the same information as dante about V identity didn't came to this conclusion and begin to ask what the hell just happened, while dante got to the right conclusion...
So I personally think that dante knew That V was a part of vergil but dosent express himself about it because he think That maybe V intention are genuine and he is good now, or maybe he played V game to see what he was up to... Also during the beginning of mission 13 when Trish reunite whit dante, she doesn't reveal the truth to Dante probably because she kwow that dante had arrived to this conclusion when meeting V, also if you watch the cutscene in mission 10 the one whit dante, Trish, lady and v arriving inside the qliphot,
V walked away, as soon as he say that he doesn't want to continue inside the three, dante and Trish look at each other suspicious, and when lady say: who was that guy? Can't belive he just run
Dante replayed very quickly whit: no one special
So probably both dante and Trish realize that something was off about V and that he could be a part of vergil, but didn't have the profe about it, Trish get the confirmation in mission 12 while dante probably realize the truth when he wake up in mission 10 and find v in front himself whit the sparda sword, or when v stabbed urizen