To me it sounds like the protagonist of the song is this kind of bad guy, but he genuinly (or at least he says so) is in love with this girl and he wants to prove it to her, that's why he says he wants to hang her name up upon a star. He says that even though he has a twisted side, there's more to him and he wants to show her, whatever it takes (hence the "if it kills me" part).
To me it sounds like the protagonist of the song is this kind of bad guy, but he genuinly (or at least he says so) is in love with this girl and he wants to prove it to her, that's why he says he wants to hang her name up upon a star. He says that even though he has a twisted side, there's more to him and he wants to show her, whatever it takes (hence the "if it kills me" part).