You should aim to have a neutral grip that feels comfortable when hitting both forehand and backhand, there shouldn't really be any rotation around the grip when hitting forehand or backhand, you should use your wrist to alter the position of the racket head rather than the grip. However that's not to say you can't move the hand up and down the grip depending where the ball is on the court. If the ball is really deep in the back corner, you may wish to move your hand up the racket to get a bit more control.

If the ball is a long way away near the front wall then you may want to drop the racket down the grip and give yourself that extra little bit of reach that may keep you in the rally. If the ball is tight to the side wall you'll want to soften your grip on the handle to stop the racket from jamming into the sidewall. The grip is such a fundamental part of a solid technique and should be adaptable depending on the situation, next time you're on court have a play and see what happens in these different situations.