In the game of the movie, there are several alternate characters that are labelled as different costumes for Emmet, even though they are just generics in the game and the film proper. However, in the film, there is a minor plot point about Emmet's face being so bland and generic he could literally be any random minifigure in the LEGO universe.
This also lends itself to another plot point in the movie: Every minifig is special and unique in Finn's eyes. In the game, there are no bland, generic names for characters as there are in the other games (Except the robots, but that's because they're the minions of the bland, boring Lord Business.) Every character, from the Bricksburg residents to the Middle Zealand guards, have catchy names.