In DMC1, Dante didn't have his own demon form. In DMC2, he did. In DMC3, they looked similar to his DMC2 one. Really, they did look similar. Black face & body, white markings on his torso, red arms and legs and wings.
Dante's new DT will probably look similar to DMC2's or DMC3's. Or Dante could just have a demon trigger that looks like Sparda's, just like the DMC1-costume Dante did in DMC3. And I think that would have greater impact in the story.
The group Nero belongs to idolizes/worships Sparda. They probably have no idea that Dante's Sparda's son, but it'll probably be a huge shock to them if he ever DT's infront of them and looks like their hero/god.