It's really all a matter of semantics.
In one sense, he's a tight end all the time, wherever he's lined up on the offense; he's a tight end playing special teams when he's receiving kicks, and he's a tight end when he's on the sideline drinking gatorade. He's a tight end because that's the position the Patriots have designated him as, and had he not extended his contract and ended up given the franchise tag, it would be for the tight end value.
In another sense, he's only a tight end when he's the last player on his side flush with the line of scrimmage (i.e. an End) while not being the furthest player from center (i.e. not a Split End.)
In this case, he'd still be a TE when motioned into the slot provided that he remains an flush with the line of scrimmage, and that he isn't the farthest outside receiving option on his side of the play.
Often, though, you'll see the Pats have Hernandez or Gronk lined up in the slot a few steps off the line of scrimmage, in which case, he's not an "End" of any sort. Depending on where he's lined up, you could call him an H-Back, slot receiver, full back, or even flanker. Less often, you might find Hernandez lined up flush with the line of scrimmage, and the furthest split receiver on his side, at which point he'd be lined up as a split end.
