The official names of celestial bodies are determined by the International Astronomical Union. They look down on companies selling star names, and your idea seems like the same sort of thing.
According to the IAU, the official names of the bodies discussed here are Earth, Moon, and Sun. Names such as Terra, Luna, and Sol are not official.
My son calls it Sol. But his mother speaks to him in Spanglish and tells him not to look directly into el sol (Spanish for sun).
Moon=Luna.
I hardly ever understand the little one. Damn Spanish.
The rain is Tess,
the fire’s Joe
and they call the wind Maria.
I’ll check back to see if they have a name for the sun.
I thought our planet was named Gaia?
Then again, since we’re terrestrial creatures, then Terra is the correct name.
But wait, we’re humans, so shouldn’t our planet’s name be Huma?
Oh, no, waitasec, we’re Earthlings to the extraterrestrials so Terra Firma is Earth!
Hi, I’m a human being, and I come from Helios-3.
Now that you mention it, the Sun’s name must have been “Always Shinin’”:
Not that I seriously believe this will ever happen, but what happens if we colonize the solar system, and the sun’s just a bland yellow star in a constellation can we look at from there?
It’s more of a GD, I suppose, but it’s interesting to me whether our great-great-grandchildren would still call it “The Sun” when it’s just a little star you have to squint to see. And would they call the new solar system’s principle, for example, “Ceti Alpha”? And the new world “Ceti Alpha V”?
If not… if the sun is always the big bright object in the daytime sky, no matter where you are, don’t we need a name for the sun that would stick from any point of view? Isn’t it kinda darned heliocentric to do otherwise?
Wouldn’t the naming rights to the moon belong to the guy who owns it?
http://www.planetaryinvestments.com/
i think the generic term moon (for example) comes from the similarity of other moons to our own Moon. like wise i think colonist of a planet orbiting alpha centari would call it a sun, but back here on good old earth we would call our source of light the Sun, or maybe not. they might just call it the star.
When or if we ever start colonizing enough to need to make the distinction, I suspect we will use Sol and Luna and Earth as proper names, and sun and moon and planet/world as generic terms. A sun will be the primary star (or stars) of your system. Not because Sol and Luna mean anything different than Sun and Moon, but because we’ve used sun and moon so generically that it will be easier to accept a distinct name. Earth pretty much is accepted in common usage as a proper name, with planet the more general term.
Then again, we have to redefine what a planet is. 
Staff Report: What is the proper name for the sun?
That started in alchemical writings. Classically, there were 7 known metals and 7 astrological planets. These were equated and alchemists routinely wrote the Latin name of the planet when talking about the metal. In fact, that’s why quicksilver’s name was changed to mercury.
Most of the named stars have Arabic names, not just the occasional interloper. The planets have Latin names, but I think most of the satellites are Greek. Except for Uranus’s satellites which are Shakespearean.
So if we’re following these traditions, we’d find out what the Arabs call the sun and give it that name. Ditto for the moon and its Greek name, which is Selene, I believe. Terra is the Latin name for “earth, land”; orbis terrarum meant “the whole world”. Tellus also meant the whole world.
I could be wrong, but I can’t think of a modern scientist ever calling it Sol in any textbook, article, or presentation. Ditto Luna. It’s always the sun, or the Sun.
I think you’d be hard pressed to find a constellation that would include a naked-eye Sun. From what I understand, the Sun’s not all that impressive an object and isn’t really visible from a few light-years out.
Lay some Arabic star names on me.
OK.
Achernar From Arabic ‘end of the river’ referring to Eridanus
Betelguese Arm pit (really) of the hunter (Orion)
Rigel Foot (again of Orion)
Deneb Tail of the hen
Depends on your definition of “few”. Within about 6 to 8 lightyears, the sun would be one of the brightest stars in the sky. IIRC, its absolute magnitude is 4.4, which means it will be naked-eye visible, although not very bright, at 33 lightyears (10 parsecs).
Algol (Beta Persei) translates as “demon star” because it is a naked-eye variable.
Alphard (Alpha Hydrae)
Alphecca (Alpha Coronae Borealis)
Altair (Alpha Aquilae)
und so weiter…
(and MonkeyMensch types faster than I do
No, we just call it “ground,” or “dirt.”
Seriously, of the few other languages I know much of, the word for the planet we live on is the word for the ground. Or for dirt. We don’t call them “earthworms” because they’re not from Alpha Centauri, you know.
LOL Thanks for the laugh.
Seriously, though, I can vouch for German and Spanish. Same deal.
Mailbag: Do other languages call Earth “Earth”?
Except it’s not all that helpful. Too much condecension, not enough understanding. There was a thread on the topic if you want to look it up.
moriah said:
Nah, only metaphysical religious nuts call it Gaia.
dtilque said:
Thank you! In the Doc Smith book series of The Lensman, Earth is referred to as Tellus. I always wondered where he got that, considering every other science fiction author in the known universe (or so it seems) calls it Terra*. Now I know.
*Except Asimov, who calls it Dirt. Gotta love that Asimov.