Who is Joseph Gordon-Levitt's character in The Dark Knight Rises supposed to represent? Is there a character in comics for him? Is he Robin?
The legal name of the character John Blake was revealed as Robin. This doesn't 100% guarantee that he'd be the Batman's sidekick Robin, but it's actually a hint. John Blake was given the access to the Batcave at the ending of The Dark Knight Rises, implying Bruce intends Blake to continue his legacy.
In the comics, Dick Grayson (the original Robin) has assumed the role of Batman on more than one occasion.
Joseph Gordon-Levitt has explained the mysterious ending in The Dark Knight Rises, in which his character John Blake was not only revealed to be called 'Robin', but also set up as the successor to become a new iteration of Batman.
It is clearly hinted by the creators that his character is actually Robin. You can check this IMDb link which further approves that Joseph Gordon Levitt's character is indeed Robin since his legal name is Robin.
Christian Bale has stated that he would not play Batman if Robin appeared anywhere in the trilogy. Christopher Nolan agreed not to include Robin, as it would undermine the dark tone of his series. At the end of this movie, Detective John Blake's (Joseph Gordon-Levitt's) legal name is revealed to be "Robin", and he quits the Police force, and is shown to enter the Batcave by following the instructions presumably left by Bruce Wayne in his will.