Our solar system is somewhat unique in it's name is the Solar System. Other solar systems are named based on their primary Star/Sun. Just like our moon is named Moon while other planet's moon(s) would have their own unique names.

Consequently, the title saying Sins of a Solar Empire doesn't directly reference an empire in our solar system.

Interestingly Sol is not an official designation for our sun. Luna is also not an official name for our moon. Sorry, but the Latin terms aren't officially the names for these entities. Now if you speak latin you might say Luna or Sol but again it's not THE official name.

And for funsies, The Sun is in The Solar System which contains The Earth and The Moon

Our solar system also contains ~146 known moons with more being verified.

Our galaxy, i.e. The Galaxy, contains potentially billions of solar systems.

Fortunately, we only have one sun and one earth in our solar system.

And no Earth is not named Terra in case you were wondering.

Yep, it's a useful thing in video games having unique names for our sun, planet and moon