Systems are typically referred to by the name of the most important planet, moon, colony, or station in the system. What qualifies as "most important" is generally based on history and tradition. In most cases, the system is named for the first colonized planet or moon in the system.
When other bodies in a system are mentioned (in news reports or personal stories), they are referred to as "the star in the Illyria system" or "a moon of a gas giant in the Kiyose system."
Below are brief descriptions of each system, including its millisector. Millisectors are not named but rather denoted by their coordinate in the overall sector, in X:Y:Z format. X is the spinward coordinate (0 is farthest spinward), Y is coreward coordinate (9 is closest to the core), and Z is elevation above the imaginary bottom of the cube.
Descriptions that are just bullet points are drafts and subject to change. Prose descriptions are more set in stone.