My answer to this question:
Another possibility is having a planet with many moons of almost totally identical size which are equally spaced in a ring around the planet. The moons all share the same orbit, equally spaced.
The PlanetPlanet blog has a post:
It references a scientific paper showing that a number of equal mass and equally spaced objects can share the same orbit and be stable.
According to their calculations seven to forty two objects could share the same orbit.
Thus your planet could have seven to forty two equal moons equally spaced along a single orbit.
Of course it seems extrmeely improbable that such a system could form naturally, so perhaps an advanced civilization assembled those mooons and placed them in orbit around the planet.
How will the people of the planet tell the difference between one moon and another if they have similar masses and thus diameters?
If the moons are less than a few hundred kilometers in radius they can be irregularly shaped and perhaps each moon has a different irregular shape. They will have to have very low orbits for their shapes to be clearly seen from the surface.
If the moons are larger than a few hundred kilometers in radius they will probably be roughly spherical and look round to the eye. But they might have maria as on Earth's moon and thus different patterns of light and dark on each moon.
And possibly the hypothetical civilization which hypothetically created that moon system helpfully coated each moon with materials of a different color.
And possibly the hopothetical ciilization might have built giant flashing beacons on each moon, with each moon's beacon flashing a different color or a different pattern.
if there are 7 to 42 moons equally spaced along a circle 360 degress around the planet, the average angle between moons will be be about 8.57 degrees for 42 moons to 51.42 degrees for 7 moons.
Thus if an arc of more than 8.57 to 51.42 degress along the orbit of the moons is visible in the sky of a location on the planet, more than one moon should be above the horizon at any one time. On the sea or a plain, the visible sky should cover 180 degrees, and so about 3 or 4 moons if there are 7 total moons, to 21 moons if there are 42 total moons, should be visible at any one time.
Possibly the story could be set in a deep valley or an urban canyon with only a limited view of the sky.
Making the moons as few as possible would make them farther apart along their shared obit and reduce the problem of having more than one moon visible at a time.
If the moons are very small they will have to have very low orbits and thus they will not be visible from a full hemisphere of the planet at any one time.
Phobos, the inner moon of Mars, is so low it cannot be seen from an entire hemisphere of Mars at once.
Because it is close to the surface and in an equatorial orbit, it cannot be seen above the horizon from latitudes greater than 70.4°
So phobos is visible from a circle 140.8 degrees wide, intead of 180 degrees wide, on the Martian surface.
I note that such a low moon would probably have an orbital period much less than a day of the planet.
And it is possible that the atmosphere of the planet is thicker than that of Earth (but not too thick for humans or natives of the planet with similar requirements. See Habitable Planets for Man Stephen H. Dole, 1964 https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf).
You may need to increase the total density of the atmosphere, and/or the amounts of various gases and atmospheric dust, and/or air pollution, to make it scatter a lot more light, while still being breathable for humans or natives with similar requirements.
If the atomosphere scatters enough light, the moons may not be visible during the day, and maybe even visible during only part of the night. Possbily even at night the atmospheric haze hides the moons near the horizon and they have to be high in the sky near the zenith, to be visible. And of course at night the Zenith may include the planet's shadow.
So possibly the area of night sky where the haze is thin enough to see the moons is less than 51 degress wide and there are only 7 moons spaced 51.42 degrees apart. So there will never bee two moons within the visibility zone around the zenith at the same time. And possibly the moons orbit at such a distance that the planet's shadow fills a large part of that region around the zenith near midnight, so that a moon wiil be visible for much less than all 51 or fewer degrees.
I think for this to work the moons will have to orbit at near, but not exactly at geosynchronous orbit, so that the 51 degree cone of the night sky where they can be seen will not sweep over two or more moons during the night. But the orbit of the moons has to be far enough from geosynchronous orbit that the 51 degree or less cone of visibilty will sweep over a different moon each night.
The length of the planet's orbit around the star may also have to be adjusted to make this work.
The mass of the planet, and the distance of the moons from the planet, will determine their orbital periods. And you will need to work out a day length and an orbital period which will result in a different moon appearing in the night sky each night for a period of about a week or whatever.