Bingo. Nolan's interpretation of Batman was more rooted in realism than the movies that preceded it, which is why you never saw characters like Clayface or Killer Croc. Why would it have been necessary to call Selina by her alias? There were visual clues to it without being overt, like how her infrared glasses flicked back in the shape of cat ears. Just like with Batman, everything about Catwoman's outfit stemmed out of function and not ornamentation.
I know for a lot of people Michelle Pfeiffer's Catwoman was the penultimate portrayal-and maybe there's a bit of nostalgia playing into it-but take it from somebody who has read the various comic storylines, Nolan's take is closer to the root of the character. If it hadn't have been, you would have seen me in here bitching about it.