Yes the moon does change shape. That is why phases of the moon happen. If you did not know, but phases means changes. So phases of the moon is changes of the moon.

The moon's shape would change with the impact of meteor's, changing the moon's landscape.

The moon supposedly "changes shape" all the time, as the moon is constantly orbiting the Earth however the moon doesn't actually change shape, it is the amount of the sunlit side of the Earth that we see changing.

The moon never changes shape only the light you can see.

How did the dirction of the moon change over time? How did the dirction of the moon change over time?