Usually people awake with a stiff neck primarily due to pillow usage. If you use too hard of a pillow or too many pillows, you can find yourself sleeping with your head tilted upward (think: trying to touch your chin to your chest), which can make the neck muscles stiff after a few hours.

Another factor may be what you do during the day. If you sit at a desk looking down at papers all day, your neck will probably be stiff in the morning whether you like it or not. The natural posture for the neck is straight up and if it is not in that position, the muscles in the neck are forced to bear the weight of your head, causing eventual fatigue.

I would say get a new pillow