Alt: Terminology
Terms used in scientific literature for subsatellites include "submoons" and "moon-moons". Colloquial terms that have been suggested include moonitos, moonettes, and moooons.
Picture of a gray, pitted moon with caption: Artist's concept of rings around Rhea, a moon of Saturn
Comments
Moooooo x [10 to the nth] n?
To name the moons of a moon of a moon of a moon of a moon....
The cow jumped over the moooon
Consider: MOONOONS
Terms used in scientific literature for subsatellites include "submoons" and "moon-moons". Colloquial terms that have been suggested include moonitos, moonettes, and moooons.
Picture of a gray, pitted moon with caption: Artist's concept of rings around Rhea, a moon of Saturn
https://www.youtube.com/watch?v=50xuuEolLR8
So it should not be necessary to name a class of moons of moons of moons.