You’ve no doubt heard some star names such as Polaris the North Star – or Betelgeuse in the constellation Orion. But, although it’s also a star, our sun doesn’t have a generally accepted and unique proper name in the English language. We English speakers always call it the sun.
If ‘Sun’ were the sun’s name in English, we’d always see it capitalized. It would be a proper noun, which is defined as “the name of a person, place or thing.” Although astronomers themselves do tend to capitalize the word sun (also moon, solar system, galaxy and universe; more about this below), most dictionaries don’t.
On the other hand, some experts say you would capitalize the word sun according to the context in which you were using it. For exmaple, you might use this sentence: “Are all suns as hot as The Sun?” Notice that, in this usage, the word “the” is capitalized, too.
You sometimes hear people use the name Sol for our sun. If you ask in a public forum like this one (see the comments below), you’ll find many who swear the sun’s proper name is Sol.
Sol is the Roman equivalent of the Greek sun god Helios. And maybe in earlier times people did actually use these names. According to straightdope.com, the first cited use of Sol as a proper name for the sun is the 1450 Ashmole Manuscript Treatise on Astrology, which stated:
Sol is hote & dry but not as mars is.
But neither Sol nor Helios is an official name for the sun, according to the International Astronomical Union (IAU), the international body of astronomers which since 1922 has charged itself with the responsibility for naming celestial bodies. Just to confuse things, the IAU does suggest we all use Sun and Moon, rather than the lowercase sun and moon. As a result, most astronomers do capitalize these words (frequently along with other non-standard capitalizations such as Galaxy, Solar System and Universe), but most media organizations (which tend to use media stylebooks such as the AP Stylebook) don’t.
So people don’t agree on whether the sun has its own name, or what that name might be. Meanwhile, the sun does have a symbol that’s exclusively its own. The sun’s symbol is a circle with a dot in the center – used in mathematical formulas.
If it is nameless, our sun has company. There are several thousand stars visible to the eye, and only a few hundred of them have actual names, as opposed to designations. Astronomers use the Greek alphabet to order visible stars in each constellation, according to their brightness. To identify stars invisible to the eye, astronomers turn to star catalogs, which assign a number to each star according to its position in the sky.
Nowadays, we know there are planets orbiting many if not most stars. Most extrasolar planets haven’t yet been given proper names either, and the IAU has gone back and forth on its decision to name or not to name extrasolar planets.
When all is said and done, whether you believe our sun has a name comes down to the language you speak, to whom you give the authority to name objects in space, and to your personal preference.
Bottom line: The International Astronomical Union hasn’t sanctioned an official name for our sun, and our sun doesn’t have a generally accepted and unique proper name in the English language. But, in history and in other languages, the sun does have proper names.