This is a total coincidence, but I just ran across this introduction to the paper New Synchronous Orbits Using the Geomagnetic Lorentz Force (Brett Streetman and Mason A. Peck: Journal of Guidance, Control, and dynamics, Vol. 30, No. 6, November–December 2007):

In a repeat-groundtrack orbit, the subsatellite point traces out a recurring pattern in some integer number of orbital periods. Traditionally, these orbits are achieved by adjusting the period of a satellite such that it completes an integer number of revolutions in exactly an integer number of sidereal Earth days.

So it seems that the term "repeat-groundtrack orbit" might be a suitably all-encompassing term for Earth orbits with rational number multiples of 1 sidereal day.

Here is a bit more of the first paragraph in case someone is interested...

Geostationary and geosynchronous Earth orbits (GEOs) are perhaps the most familiar and useful examples. These orbits have a mean motion equal to the spin rate of the Earth. We shall refer to orbits that repeat their groundtrack every orbital period as GT-1 orbits. Thus, all trajectories in GEO are in the GT-1 class. A more general class, the GT-x orbit, repeats its groundtrack every x revolutions. For example, satellites in the GPS constellation are in 12 sidereal hour orbits and can thus be considered GT-2 satellites. Many low-Earth-orbit (LEO) imaging satellites designed for full-Earth coverage also use repeat-track orbits. Every 16 days, over the course of 233 orbits, Landsat 7 covers the full Earth, making it a GT-233 satellite...

This is a total coincidence, but I just ran across this introduction to the paper "New Synchronous Orbits Using the Geomagnetic Lorentz Force" (1, 2) (Brett Streetman and Mason A. Peck: Journal of Guidance, Control, and dynamics, Vol. 30, No. 6, November–December 2007):

In a repeat-groundtrack orbit, the subsatellite point traces out a recurring pattern in some integer number of orbital periods. Traditionally, these orbits are achieved by adjusting the period of a satellite such that it completes an integer number of revolutions in exactly an integer number of sidereal Earth days.

So it seems that the term "repeat-groundtrack orbit" might be a suitably all-encompassing term for Earth orbits with rational number multiples of 1 sidereal day.

Here is a bit more of the first paragraph in case someone is interested...

Geostationary and geosynchronous Earth orbits (GEOs) are perhaps the most familiar and useful examples. These orbits have a mean motion equal to the spin rate of the Earth. We shall refer to orbits that repeat their groundtrack every orbital period as GT-1 orbits. Thus, all trajectories in GEO are in the GT-1 class. A more general class, the GT-x orbit, repeats its groundtrack every x revolutions. For example, satellites in the GPS constellation are in 12 sidereal hour orbits and can thus be considered GT-2 satellites. Many low-Earth-orbit (LEO) imaging satellites designed for full-Earth coverage also use repeat-track orbits. Every 16 days, over the course of 233 orbits, Landsat 7 covers the full Earth, making it a GT-233 satellite...