It has all those different names because there is more than one culture on this planet. Most sun myths (and myths in general) are not only entertaining tales, but insightful archetypes for the human condition and psyche. I personally find it abhorrent that people dismiss such myths as archaic and primitive just because we have "science" to enfold us under it's wing and teach us everything.
There are many diverse sun myths, some cultures have similar myths (eg Inca & Maori, the people are not getting enough sun so a hero does something about it), but what alot of them have in common is that the sun is responsible for either creating humanity, or teaching it the secrets of civilisation.
Norse mythology gives us Freyr, who visits his wife in the underworld giving us winter, but also symbolising the polaric swinging from light to darkness and back. This is reflected to some degree or other in almost all myths representing the struggle between light and darkness, the Jesus myth notwithstanding.
Jesus is "the light of the world", when he dies, the sun darkens. Upon his resurrection "when the sun had risen, they went to the tomb.... As they entered the tomb they saw a young man, dressed in a white robe... he said to them 'do not be alarmed; you are looking for Jesus of Nazareth, who was crucified. He hath been raised."
The Jesus myth (and christianity in general) is not that unique. It is, similar to hinduism, a menagerie of myths, traditions and beliefs assimilated into the original judeic practise (esp. see the Cult of Mithras). Christianity derives it's central myth (jesus' birth, death and resurrection) from the most primal centre of human thought. All cultures have a similar myth, whether it is Odin hanging himself on Yggdrasil for knowledge of the runes (logos), or the phoenix dying and being resurrected from it's own ashes, the myth of Osiris, Isis and Set http://www.touregypt.net/godsofegypt/legendofosiris.htm , and the inevitable judgement day myths all fit into this way of thinking, with the world being reborn into greatness after the deluge (or war, fire, darkness).
"For the traditional culture, all that we do in our lifetimes is merely a replay of events that took place in myths... All human experience in the past derived its value from myth, which was perceived as infinitely more significant than the life of an individual." - J. F. Bierlein
. I think Sol first appeared in the SF literature (particularly in I. Asimov's writings, I could be wrong about this). Scientists just call it The Sun, so I think it's up to us to give it a name and make it stick world wide ( am I thinking to big???). 