Sorry, Kytim, but rewatch The Dark Knight. Gordon's monologue at the end clearly says that Dent was the White Knight, and Batman's the Dark Knight.
http://batman.wikia.com/wiki/Two-Face_(Aaron_Eckhart)#Two-Face "It could be argued that while
Batman Begins was the origin story of
Batman,
The Dark Knight was more Two-Face's tale. It was highly expressed that both men were effectively two halves of the same coin; one focused on justice regardless of the law while the other sought it through legal means. Both men had high respect and hope for each other, for it was mutual admiration that led both men to work together in hopes of ending Gotham's decades of corruption.
The duality that both men possess was portrayed in many tones, some subtle while others less so. Their nicknames of the White Knight and Dark Knight were respective of each other. While their needs were met, there were problems that only Batman could overcome thanks to his vigilante status, while at the same time, only Harvey Dent could deliver legal justice and cement Batman's efforts. Without Dent, Batman's capture of any criminal would be little more then a revolving door, as the legal system would otherwise be corrupted and used at the whim of the mafia.
Again like Wayne before him, Harvey's transformation into Two-Face was marked by a tragedy. Whereas Bruce Wayne's loss of his family triggered powerful vengeful emotions which he eventually overcame, Harvey never had the time to resolve the intense feelings of loss he felt at the death of
Rachel Dawes. Thus, while Wayne's transformation into Batman resolved these emotions from negative to a more positive light, Dent's transformation into Two-Face was more the opposite, poisoning his once decent intentions. However, neither man's reaction to the tragedy could be described as mentally healthy, an unfortunate fact that
the Joker constantly tried to make Batman realize and accept (Although the Joker's role in Dent's descent by making contact with Dent at an emotionally and mentally difficult time should be taken into account)."
If this is the case then the title Dark Knight is refering to Harvey Dent falling to his darker side. Of course the writers wanted the story's themes to criss cross one another, so there are many different interpretations to discern from the plot. I do agree with the idea that Two-Face and Batman are two side of the same coin( no pun intended). Ironically I found the ending of the movie to imply that Batman was actually the White Knight because of his good intentions for Gotham, but had to take on the Dark Knight image(to the public) to preserve the balance of the city. Harvey, on the other hand, was pepped up to be the White Knight, but became the Dark Knight when he gave into his primal nature.
You could also argue that the Joker was trying to convert Batman from the White Knight(inability to kill) to the Dark Knight. This is why the Joker had been taunting Batman to kill him several times in the film. when Batman took the blame for the murders conducted by Two-Face, the Joker, in a way, succeeded in this endeaver.