I don't think you should feel any pressure to change it. The Solar System belongs to the writers just as much as it does to the physicists and unless your target audience is specifically physicists, then the average visitor of your site will be more likely a consumer of sci-fi than a practitioner of physics.

The argument is rather pedantic to me since the word Sun comes from the old English, Germanic, and European, whereas Sol comes from the Latin, Helios from the Greek, svár Sanskrit, etc. They are all valid names for our local star.