Two aspects of this are under the total control of the creator of the universe:
True, but that doesn't help a reader find the Universe, which was my point.
Thinking Horndog named his universe The Swarm Cycle, then he and other writers started using the phrase A Story in the Swarm Cycle Universein the story listings with a lower-case 'the', readers will look for the universe under S, not T.
While it is not relevant to the issue, I haven't written a story and posted it in someone else's Universe. So I don't know how that Universe reference is created or assigned to the stories of an Author who is approved to post in someone else's Universe. From what you said, it sounds like the Universe's creator writes the phrase and invited Authors just select if from the list of universes they are authorized to post to while posting.
Perhaps Universe owners should use the Universe name they assigned the universe. I hadn't thought of the issue until now, so I think I will mention the matter to him. What he does with my feedback is his decision.