Punk is a rather wide term. Everything from emo to rock to goth to metal, they are all sub-branches of the overall punk-movement. And it is quite popular nowadays to have a more punk'ish look, as several of you have mentioned, Rihanna's style has been punk'ish recently, even if she is a pop/RnB singer. However, the punk-movement has been alive a loooong time before Rihanna took that style upon herself.
It's a valid guess CoolDemon is coming with - that Dante has been summoned to help out this group of rebels to fight the power - the demons who rule the world of Limbo. And it is also a valid guess that the girl, and maybe the other members of said group, have a punk'ish look about them which is also reflected on Dante's new look. However, I am still unsure if CoolDemon's blurry screenshot of the girl is actually showing her head and hair like that - I still think it looks like a hood. We'll hopefully get to see some clearer shots of her soon so we can get a good look at her.
We're still only guessing and making theories, but I hope we will get some story info soon. Personally, I am starving for some story information. We only know the gist of it so far and I really hope there will be more to it than just "Dante fighting the bad demons" or else I'll be really disappointed, especially seeing as creating an interesting storyline is supposed to be NT's forte.