Why does the Moon change shape?

It does not. The Moon is always a whole sphere, and the Sun is always lighting half of it. What changes is how much of the lit half we can see from here.

As the Moon travels around us, our view of that lit side shifts, from none of it to all of it and back again, over about twenty-nine and a half days. The same face always points toward us, so the far side is not dark, only private.