Roy is still Speedy, Wally is still Kid Flash, Donna is still Wonder Girl, AND Garth is still Aqualad; but Dick is Nightwing and Jason is Robin — at least, that's how they are in 1985. If we advance the timeline five years, that may change; but I'd be against the New Teen Titans upgrading their identities as they did on the post-Crisis Earth. (I also wouldn't go more than five years, specifically to keep them young enough that codenames like Kid Flash, Wonder Girl, and Aqualad aren't that absurd.)