Is there a good generic name for large non-luminous bodies in hydrostatic equilibrium?

balls (rockballs, iceballs, gasballs...)

this nomenclature makes jokes about uranus twice as funny

If the object is in orbit around another, it is called a satellite.  There is no distinguishing terminology for a satellite that is spherical versus one that is non-spherical...  although, if the object has considerable mass compared to its primary, and the orbit is distant enough so that the barycenter of the system is outside of both bodies, the dual objects might be referred to as a binary planet.  The Earth-Moon system could eventually qualify, and the Pluto-Charon system (semantics aside... regarding dwarf planets) do qualify.

swimmers

It must be Planet.

You said Large, that excludes the moon and Pluto they are not large

Otherwise it must be

Large non-luminous bodies in hydrostatic equilibrium

I propose "dirt".