Most moons orbit in the equatorial planes of the planets they orbit. Earth's moon is a big exception.
Because of the varying tilt angles of planets, some satellite systems are too far out out the planes between their planets and their stars, and so never pass into the shadows of their planets and never get eclipsed by their planets. Other planets have axial tilts such that their moons in equatorial orbits can sometimes be eclipsed by their planets.
Here is a link to a table of the axial tilts of the planets in our solar system. The eaxial tilt of a planet can be as little as 0.00 degress or as much as 90.00 degrees. The examples in our solar system vary from as little as 0.03 degress (Mercury) to as much as 82.83 degrees (Uranus),
Amateur astronomers often view the 4 Galilean moons of Jupiter, and do things like timing when they are eclisped by jupiter. So the moons of Jupiter are often eclipsed. But Jupiter has an axial tilt of only 3.13 degrees.
If viewed from Mars's surface near its equator, full Phobos looks about one-third as big as a full moon on Earth. It has an angular diameter of between 8' (rising) and 12' (overhead). Due to its close orbit, it would look smaller when the observer is further away from the Martian equator and is below the horizon and thus invisible when viewed from Mars's polar ice caps. Deimos looks more like a bright star or planet for an observer on Mars, only slightly bigger than Venus looks from Earth; it has an angular diameter of about 2'. The Sun's angular diameter as seen from Mars, by contrast, is about 21'. Thus there are no total solar eclipses on Mars, as the moons are far too small to completely cover the Sun. On the other hand, total lunar eclipses of Phobos happen almost every night.
Mars has an axial tilt of 25.19 degrees.
So moons orbiting in the equatorial plane of a planet can be eclisped by the planet if they are close enough to the planet and if the planet has an axial tilt of 25.19 degress or less, and possibly even if the planet has a larger axial tilt.
PS the worldbuilding stack exachange is a good place to ask questions about creating fictional worlds.