This is how we call our sun and our solar least officially. It's funny that in most science-fiction stories, our sun is always named Sol and the Earth Terra. These are both good names, and have their backgrounds, but in all probability people will always be calling the Sun "the Sun" and the Earth "the Earth". It's just that we are still completely self-centered and see ourselves as unique (and frequently alone) in the universe.

Of course we do, we've never been anywhere else!

It is only logical that the sun (our sun) become THE Sun. Do not expect us to walk around anytime soon and say "Sol is shining pretty brightly today". Maybe someday, when we have expanded across such distances and so many solar systems, we MUST call a sun by its name.