General:
* Moon (the most basic, obvious term)
* Satellite (a celestial body orbiting a planet)
* Lunar body (relating to the moon)
* Celestial body (any natural object in space)
Appearance:
* Crescent (a shape like a curved blade)
* Gibbous (a shape that's more than half-full but not fully round)
* Full moon (when the moon is fully illuminated)
* New moon (when the moon is not visible)
* Disk (a round, flat shape)
* Sphere (a perfectly round, three-dimensional shape)
* Glow (the soft light emitted by the moon)
* Light (the illumination provided by the moon)
Effects:
* Tide (the rise and fall of the ocean's water level influenced by the moon's gravity)
* Influence (the moon's impact on various aspects of life)
* Myth (stories and legends surrounding the moon)
* Symbol (representing concepts like time, change, or beauty)
Specific terms:
* Harvest moon (the full moon closest to the autumnal equinox)
* Blue moon (the second full moon in a calendar month)
* Supermoon (a full moon that appears larger and brighter than usual)
* Blood moon (a total lunar eclipse where the moon appears reddish)
* Lunar eclipse (when the Earth casts a shadow on the moon)
This list is not exhaustive, but it gives you a good starting point for describing the moon in different contexts. The specific noun you choose will depend on the specific meaning you want to convey.