I'm not sure if anyone's mentioned this or even noticed this, but I personally don't believe Batman is The Dark Knight in this story, even though admittedly that alias is inherently his own in the comic books; but this could be a clever subtext in the film by Nolan.
“You either die a hero, or you live long enough to see yourself become the villain.”
That quote is ultimately the pretext, the main theme, behind the story. I see it as an evolution to that of which proceeded it in Batman Begins with Bruce's realisation that, in his attempt to fight the criminal underworld, he as a man is as weak and as potent as any other individual in the crowd. But as a symbol, he is more, he's just enough to make a difference. So it's no surprise that Nolan uses this form of mentality to be the ingredients for the success of his films.
After seeing the movie, the most memorable character to me was not breath-taking performance of Ledger's Joker, nor Batman's grit, or even Alfred's English wit, but I was the only one who considered Harvey Dent as the protagonist in this story. His transformation and overall meaning to the story is undeniable. He is the 'White Knight', but through his transformation, wouldn't it make more sense to identify him as the 'Dark Knight'?
Yes okay, you have an opposite to this White Knight, the Batman; they're both Knights in their own sense yet why is there a difference to justify the 'White/'Dark' metaphor? Is Batman really that dark? The one who ultimately rejects becoming that villain, and risks his own life to stay true to that principle? Or can Harvey Dent - the one who himself bought life to that quote, be seen as that Dark Knight?
In my eyes, there is simply more to justify Harvey Dent as the Dark Knight rather than the Batman. Just my 2 cents