There are eight planets. Everything else is an asteroid. That would leave moons as moons (a.k.a. satellites) and leave comets as a separate class of object. Asteroid is a perfectly fine word. No need for "minor" or "dwarf" planets or "small solar system objects."
We have main-belt asteroids, near-Earth asteroids, Trojan asteroids, Centaur asteroids, and Kuiper-belt asteroids (like Pluto) all which will be managed by the, uh, Asteroid Center.
We'll worry about extrasolar planets and "rogue" planets (loner worlds unattached to stars like the Moon was in Space: 1999) later.