Its name is the Moon

The name of Earth's moon is "the Moon". In particular, its name is not "Luna".

But they call it "Luna" in a science fiction story I read

That's fiction. They can call it anything without being wrong. In the novel 1984, England is called "Airstrip One", but that doesn't change England's name in the real world.

But the English language doesn't work like that. There's no such thing as official words for anything. Whatever word English speakers use to describe something is its name.

No, that doesn't apply to proper names. Specific people, places, and things do have official names, which can't be changed by common consensus. If we all started calling you "Betty", would that mean that your name is "Betty"? Of course not.

Also, even if that were the case, practically nobody actually calls it "Luna" or anything other than "the Moon" outside of fiction. Random people on message boards don't count. You won't find a textbook or newspaper where it's called that.

Most people may call it "the Moon", but scientists call it "Luna".

No they do not. NASA does not. Astrophysicists do not when writing journal articles (example 1, 2, 3).

Who has the authority to decide the official name of the Moon?

The International Astronomical Union Working Group for Planetary System Nomenclature, an internationally recognized group of professional astronomers. And they say:

The Moon does, of course, have a name - the Moon.

But "luna" is simply the Latin/Spanish/Italian word for "moon"

True but that doesn't matter, since I'm talking about the English name for the Moon. Other languages have other names. The Spanish word for Germany is "Alemania", but that doesn't mean the actual name of Germany is "Alemania" when you're speaking English.

But "lunar" means "related to the Moon"

True but that doesn't matter. "Fraternal" means related to brothers, but the word is still "brother", not "frater".

I don't care what's correct. I like how "Luna" sounds, and I'm going to use it, as an affectation

Fine. I don't care. Just don't tell anybody else that "Luna" is its actual name.

Coming soon