Photo Credit: NASA
Photo Credit:NASA SOHO

You sometimes hear the name Sol in association with the sun. That’s the Roman equivalent of the Greek sun god Helios. But neither Sol nor Helios is an official name for the sun, according to the International Astronomical Union.
So the sun doesn’t have its own name. But it 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.
In being nameless, our sun has company. There are several thousand stars visible to the eye, and only a few hundred of them have names. 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.
Our thanks to:
Frank Bash
University of Texas at Austin
When I was editing reports for the U.S. Global Change Research Program/Climate Change Science Program, the federal multiagency program that supports scientific research and global observing systems, we referred to the Sun and Earth, both capitalized, i.e., we treated them as proper nouns. In these U.S. Government publications, the name of the star at the center of our solar system is the Sun, and the name of our home planet is Earth. All stars are suns, but there is only one Sun.
Rick Piltz
Director, Climate Science Watch
Washington, DC
This NASA page says the sun doesn’t have a real name. http://solarsystem.nasa.gov/faq/index.cfm?Category=Sun
And it says the moon doesn’t either.
The sun does have a name – Helios
Some people call the moon Luna