I had a hard time time coming up with a name “Unified Worlds” for the main body of aligned planets and races. Anything with “United,” “Federation,” or “Planets” became too Star Trek-y. Anything with “Alliance” became too Star Wars. Plus, “alliance” felt too warlike, in that it feels to me you become “allies” when you’re banding together AGAINST someone else. I preferred the more peaceful term of “unified” since that didn’t have a connotation of battle lines.
And I know in actuality, whole worlds and planets wouldn’t join these types of organizations, as each planet/world would typically be made up of different ruling bodies, like all the different countries and governments of the real-world Earth. It starts to get confusing though to account for that many different factions, so it’s a bit cleaner to generalize races into “planets.”