Fake American: In the first movie, Katie Holmes and Morgan Freeman are the only actual Americans, amid the Welsh-born Englishman Christian Bale, the English Gary Oldman, Linus Roache, and Tom Wilkinson, and the Irish Cillian Murphy (and Northern Irish Liam Neeson, but Ra's isn't American anyway). There are more real Americans in the second film, but the Joker is played by Australian Heath Ledger. (We can't be sure of the Joker's nationality, but he speaks with a Chicago accent).
Notably, almost the entire cast of Begins (including most of the main stars) hail from one part of the British Isles or another, although Michael Caine's character is British and Ducard is a stateless individual.
This is mostly averted in the sequels, although notably the main villains of both sequels play it straight (Heath Ledger was Australian, Tom Hardy is British and Marion Cotillard is French.)
Fan Nickname: The "Nolanverse" is a common fan-used name for the trilogy.
Fans who disliked Joseph Gordon-Levitt's character being revealed to be the Nolanverse's version of Robin have taken to calling him "Not Robin".
On a meta-level, BatBale is used when referring to the actor or the character.
Before the official series name was revealed, this wiki called it The Dark Knight Saga.
Lying Creator and Actors: The statements that Talia al Ghul and Robin would not be in the films was supported (by lying, or simply silence) by the actors who played Talia al Ghul and Robin.
Earlier on, Nolan also claimed that Robin would never appear in the series because Bruce Wayne himself was just starting out, and Robin "would still be a kid at this time". This one's at least true From a Certain Point of View: there's a Time Skip before Rises, and Dick Grayson—the character almost everyone assumed Nolan was referring to—is replaced by the Composite Character Robin John Blake.