They wouldn't change Nygma's name. He doesn't have to go around the movie introducing himself as E. Nygma as Edward (or Riddler) would work fine.
It would be a silly thing to change.
Now then, in the movies Nolan is making though, don't expect to see Mr. Freeze. A guy who shoots lasers that freeze people instantly is a little too sci-fi for what Nolan is doing in his movies. Don't expect to see the Lazerous Pit or Clayface for the same reason.
Riddler, Mad Hatter, Penguin, Catwoman, Talia Al Ghul, Black Mask, Mad Hatter, Poison Ivy, the Ventriliquist and others I could see appearing ina third. But Mr. Freeze, Clayface or the return of Ra's Al Ghul are not happening.