Its name is Earth

The name of the third planet from the Sun is "Earth". In particular, its name is not "Terra".

Don't take my word for it, of course. Just look it up in the dictionary.

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

That's fiction. If Earth is called "Terra" in a work of fiction, that just means that's its name within the setting of the story. In the novel A Princess of Mars, Mars is called "Barsoom", but this in no way means that this is really Mars's name.

Fiction authors are generally well aware of this distinction. Earth is called "Terra" in Arthur C. Clarke's novel Imperial Earth, but when not writing fiction, Clarke always referred to it as "Earth". See, for instance, his textbook Interplanetary Flight.

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 "Spot", would that mean that your name is "Spot"? Of course not.

Also, even if that were the case, nobody actually calls it "Terra" outside of fiction, except science fiction fans in informal settings. In formal nonfiction publications that have undergone editorial review, it's called "Earth". Some examples:

Astronomers may call it "Earth" when they're talking to the public, but they call it "Terra" in professional journal articles.

No they do not: example 1, example 2, example 3.

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

The International Astronomical Union, an internationally recognized group of professional astronomers. And they say:

The eight planets [in the Solar System] are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

But "terra" is simply the Latin/Portuguese/Italian word for "earth"

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

But "terrestrial" means "related to Earth"

True but that doesn't matter. "Cardiac" means related to the heart, but the word is still "heart", not "cardia".

But the word for people from Earth is "Terrans", right?

Not in the real world, no.

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

Fine. I don't care. Just don't tell anyone else that its name isn't "Earth".

See also