Yes, the moon does rotate. It's rotational period matches its orbital period - that is referred to as tidal lock. If it did not rotate, we would see the entire surface as it orbited the earth.
Try an experiment with a couple of balls - mark each one and then move one in a circle around the other, keeping the marks lined up. You'll notice that the ball in "orbit" completes one rotation about its axis for each "orbit" it makes around the other ball. The try it again, keeping the mark on the "orbiting" ball lined up with a point somewhere else in the room. You'll notice that the orbiting ball continually presents a different side of itself to the ball it's circling as it orbits.
The same thing is happening to the Earth-Sun system. The Earth's rotation about its axis is very gradually slowing down, and eventually the Earth will be tidally locked to the Sun and one side of it will always face the Sun while the other side will face away. But that won't happen for a few billion years.
Give me a break. From the Earth's perspective it does not rotate. We don't see the other side of the moon.
Yes, you can give me all kinds of scientific evidence that it rotates from some objective perspective other than our own, but when you're making that argument remember that it's bullshit to everyone living on the planet who sees the the same face of the moon for all their life.