There really isn't any equivalent of the asteroid/planet split that exists for non-moons. We've known about small, non-spherical moons for over a century and n

There really isn't any equivalent of the asteroid/planet split that exists for non-moons. We've known about small, non-spherical moons for over a century and nobody has seriously advocated giving a different name for them and the big spherical ones: Luna, Callisto, Ganymede, Europa, Io, Titan, and Triton. But yeah, astronomers will certianly need to figure out some distinction between chunks of ring and discrete moons.