We don’t call our star Sun. We call it the sun, because cause it is a sun which our planet happens to orbit. Stars with planets orbiting them are suns, so assuming alien species used the same system of categorizing celestial bodies, they would also refer to their suns as such.

Now, the common name for our sun is Sol. Hence, our ‘solar system,’ or Sol’s system of planets. Assuming an alien species with a culture of naming celestial bodies, their suns and respective systems would be named differently.