Trans-Neptunian objects
Even asteroids have names, e.g. Ceres. But lumping them all into a named category, i.e. planet vs. non-planet, is the issue. And I think it's already been done with "Trans-Neptunian" which includes pluto. Just like the "Asteroid Belt" includes Ceres.
There shouldn't really be a debate because it's obvious that there are millions or trillions of objects in the 250,000 AU radius cloud that surrounds the Sun. In a billion years when we've visited them all with probes, I'm sure each one will have a bar code painted on it.