Yes, the moon does change position in the sky throughout the night. This is because the Earth is rotating on its axis as the moon orbits around it. As the Earth rotates, different parts of the planet are facing the moon at different times, causing the moon to appear to move across the sky.

The exact position of the moon in the sky will depend on your location on Earth and the time of night. For example, if you are in the Northern Hemisphere, the moon will appear to rise in the east and set in the west. In the Southern Hemisphere, the moon will appear to rise in the west and set in the east.