For star rotation timelapse shots like what we see in the OP, the rotation period is sufficient. Since we're on airless planets, you can see all the stars whether it is day or night, so the presence or absence of a sun is irrelevant.
If the sun is up, the blurry-shadow effect of the sun moving against the sky might be wanted, or unwanted. If you want the sun to be in a fixed position, you want to find a planet tidally locked to the star - which in most cases would either give you an uncomfortably long day, or be so close to the str that the background sky would be lit by the star (which, again, might be a wanted or unwanted effect).