Look. In the episode Fractured, Larry, Robin's reality-bending midget clone said his name was Nosyarg Kcid, which is Dick Grayson backwards. Only Dick Grayson's Robin becomes Nightwing (How Long Is Forever), from TV, comic, or otherwise. Only Dick's Robin had a thing for Koriander, Tamaranian Princess (aka Starfire). And as we (and Raven) saw in Haunted, the infamous plunge of Robin's folks and him swearing the oath to become Batman's protege and partner is the origin of one Dick Grayson.
As for the long pants and whatever, Dick wore the exact same costume during his last run on Batman: The Animated Series, because the FCC frowned on his 60's "Holy...Batman" attire.
Onto the staff...it is pointless because anyone can use it. Heck, Robin's not the only one to use it, for Slade (alias Deathstroke) uses the staff frequently, whereas in the comics, he prefers (and is allowed to have) guns and other dangerous firearms that are not suited for children.
Another thing to add is that this show is based off the Wolfman and Perez era of the Titans (the second incarnation), and on the second team, there is Dick Grayson (Robin), Koriander (Starfire), Garfield Logan (Beast Boy/Changeling), Raven, and Victor Stone (Cyborg). Hints were given to their secret identities in varying episodes (for Cy, Deception and part of The End pt.2 were his hints).
Besides, when someone asked at the comic con about Robin's identity, at first it was thought that Robin was a combination of all three, but now, all the creators say is "Watch Fractured" and in that episode, Robin is Dick Grayson, and as such, Teen Titans (TV series) Robin is Dick Grayson.