moonmoons
submoons
moonitos
moonettes
moooons .. “IAU [International Astronomical Union] will have to decide!” Kollmeier told
Quartz.
Not able to access New Scientist paywall either, I understand the theory says if the submoon is very much smaller, the parent moon very much larger and has a high orbit from the planet, it will win the gravitational battle for the submoon, otherwise the planet wins or the moonette breaks up.
No known minimoons in our solar system but apparently four do meet the requirements for a parent: Callisto, Titus, Iapetus and our own, though ours of course isn't a 'natural' (accretion) satellite and as such is moving away from earth. This can disrupt the survivability of moonettes,
https://www.sciencealert.com/can-a-moon-have-a-moon-kollmeister-raymond-submoon-moonmoon
