Just curious, can moons have moons?
Galaxies can have stars, stars can have planets, planets can have moons.
Can moons have their own satellites?
And if so, can those satellites have their own satellites?
What is the physical limitation of such relationships?
The short answer is yes. But there are limitations.
The Earth’s Moon is too close to the Earth to have any stable orbits around it. But if the Moon were ten times as far from the Earth as it is, then it could have moons of its own.
(As an analogy, the Sun has planets, and those planets have moons, so second-order orbits are possible.)
Unfortunately, moving the Moon to 10 times its current distance would put it at 3.8 million kilometers away. Since the Earth’s Hill Sphere is only 1.5 million kilometers out, that would be an unstable orbit for the Moon and it would soon be lost to solar orbit.
Orbits around the Moon are always very unstable. This is due to mascons on the Moon which make its gravitational field rather lumpy. Combine that with tidal effects from the Earth and Sun and anything put into Lunar orbit won’t stay there for any great length of time.
Moonlette
How about Secondary Moons?
We just have to call them “moonies”
Third-order, or higher if our galaxy is rotating around a cluster or supercluster 
Nope
Earth: 5 letters
Moon: 4 letters
Moon’s moon: 3 letters - suggestion: Nub
Moon’s moon’s moon: 2 letters - suggestion: Ir
Moon’s moon’s moon’s moon: 1 letter - suggestion: O
Moon’s moon’s moon’s moon’s moon: 0 letters - suggestion:
That’s all ridiculous. If you had that many moons in a row, you’d have a moon river.
And if they all hit your eye like a big pizza pie, either the pain of the impact or the lovestruckness will render one lachrymose, so it would also be Crimea River.
Won’t somebody think of the cow jumping over the moon?
Maybe a moon’s moon could be a “moo”, in honor of the cow.
I suggest “filia”, the Latin word for daughter. Then, if someday we found a rock orbiting a filia orbiting a moon orbiting a planet orbiting a star… we could call that rock a granddaughter, “neptem” in Latin.
But it would be wider than a mile.
Which six letter name do you want to replace Sun/Sol with?
Just call it Dat Sun.
There is already an automobile by that name.
So now that yellow thing in the sky is a Nissan?
Well, such a secondary satellite would likely be relatively small…
“moonimal”.
Helios. Duh!