The Sol system ("Sol" is pronounced with a short-O) is the
planetary system of the star Sol, which is usually called "the sun".
The Sol system is usually called "the solar system".
The problem with the name "solar system" is that the O therein is
pronounced as a long-O, and the "-ar" suffix does not fit with most
star-names.
Just as there is the Sol system, there is also the Proxima Centauri system,
the Barnard's Star system, the YZ Ceti system, the Lalande 21185 system,
and menny other planetary systems in which the star's name ends with a number.
Notice how with most of these star-names, the "-ar" suffix does not fit.