See, this is part of the problem I was talking about. The name Robin has connotations to people who know the Batman mythos. They know the relation that the character Robin has to the character Batman, so attaching that name to a character instantly creates a connotation. And if you're attempting to make a character into a new Batman, then attaching the name Robin to him, in any context, muddies that. In fact, it's probably the worst thing you could do, short of revealing that his real name is Oswald Cobblepot.

But still, I thought it was quite obvious that he was supposed to be the new Batman, not only with the quite transparent visual references when he reaches the Batcave, but also his obsession and idolatry of Batman throughout as well as the ever-present theme of Batman being a symbol that can exist without Bruce Wayne. If Blake becomes anything other than Batman, then that point is left unresolved. So I thought that was told quite well, barring the unnecessary bit of fan-service that threatened to destabilize that message.

EDIT: Oh, I almost forgot one more opinion. See, I like that they didn't name him Terry McGinnis or anything else like that because it seemed they were going for subtlety in regards to his role. Yes, I had a feeling he was in there to be a Batman successor before I even saw the movie, but with an innocuous name like John Blake, I couldn't be sure. And I liked that. The movie throughout gave just enough clues that he COULD be something like that, but he didn't necessarily have to be. You name him Dick Grayson, Tim Drake, or Terry McGinnis, and you're kinda locked into that, and so is the audience. That could be another reason I find naming him Robin such a mistake, because in a way it kinda undoes that concept, even though it was thankfully not there until the end.