What to call a collection of planets?

Solution 1:

Depending on how you wanted to go, I would suggest either "system" or "federation"

• A "System" of planets brings to mind a solar system. While these aren't necessarily orbiting the same star, they are in the "political orbit" of another, and the analogy would be clear.

• A "federation" of planets would probably bring to mind Star Trek for some, but likewise, the intent would be clear.

• Finally an "Empire" would suggest total domination and subjugation. As such, while the analogy would be clear, it may be harsher than desired.

Solution 2:

In the context of a space game, with its sci-fi implications, the common way to refer to a collection of planets in association with their star is: Stellar system.

"Solar System" has a specific accepted instance, which is to say the collection of planets associated with the star named "Sol", called "The Sun" in common parlance.

ETA: in light of what @AffableGeek has written, I see that I probably missed the questioner's intent. So let me add:

Confederation