What is the official term for a relationship between a planet and its moons? Sorry if this is a dumb question, I could not find anything naming this in my astronomy books, and Google searches only seemed to show me pages about astrology, [sarc] because naturally, human relationships are influenced by celestial bodies. [/sarc]

I'm thinking along the lines of a parent-child relationship or a symbiotic relationship, but I couldn't find anything that specifically names this kind of relationship.

Is there an official term for this relationship?
I don't believe there's an official term but there are a few familiar/common terms.

Parent Body/Satellite is one.

Central Object/Orbiting object or Central Object/Satellite.

Star/Planet or Planet/Moon imply one orbits the other.   For a non orbiting Moon or Planet "Rogue" is used before their name.

A grey area comes into play when the two objects can be considered binary as opposed to one orbiting the other.   Some people define a binary orbit as one where the barycenter is outside the body of the more massive object, but I don't like that definition because by that definition, Jupiter and the Sun are a binary system and the Sun weighs 1100 Jupiters.   The Sun also has planets that don't meet that criteria, more distant than Jupiter.

Another problem with the Barycenter outside so it's binary argument is that when a star dies and goes white dwarf or even denser, then pretty much every planet now orbits a barycenter outside the star, but when it was a main sequence star, this wasn't the case.   The orbits didn't change, just the size of the central object.  That shouldn't change the definition of the orbital relationship.   I think the Barycenter argument, while convenient, is highly flawed for that reason.

Pluto/Charon could be called a binary dwarf planet, but because Charon was likely created from a collision on the Body that's now Pluto, I think that's a poor definition and I think Charon should be called a moon or collision moon.   That said, because four tiny moons orbit both Pluto and Charon, calling them a binary-system has some merit too.  There's no neat and tidy way to make a precise dividing line, besides the barycenter, which is neat and tidy, but as I said above, inaccurate.

Asteroids are sometimes found orbiting one another and I rarely hear that defined as a central asteroid with a smaller asteroid orbiting it, it's more often called a binary asteroid.  I've never heard it called a baby asteroid orbiting it's parent, but again, definitions fall into a grey area if one asteroid is quite a bit larger than the other.

This XKCD comic addressed circumbinary orbits and "the other kind", which doesn't have a name.   Not everything needs a name, and in this case, I don't there is an official one.  "Central body" "Central object" or "Parent" work just fine as familiar and common terms.