Yes. The “phases” we see on celestial bodies - especially the moon, but also visible on planets like Venus - are caused by the light from the sun falling on one side of the body, so as their position relative to the sun changes, the “phase” will change.
The moon is tidally locked to the Earth, so unlike when we observe the moon from the Earth when it moves across the sky, the Earth will stay roughly in one place in the sky if you’re observing it from the surface of the moon. Actually if you took a timelapse you would see it wobbling a little, but it wouldn’t rise and set as the sun and moon appear to from the Earth.