Region: Middle Earth
I remember this now! Primarily because of the movie scene (I'm sorry! I only remember 'The Beacons are Lit! And Rohan shall answer' scene in the movie)
Anyways, to answer the original question, Lindon-Rivendell, I believe the way the relationship between Independent Rohan and U.S.G. is set up, it's very similar to the Oath of Eorl but different. In my personal countries lore, a civil war was fought, the United States of Gondor emerged, with some portions of Rohan joining, the remaining portion of Rohan was asked if they wanted to join as well. But Rohan said, "No, we're good. But we'll remain friends" So the part of Rohan that remained independent became known as Independent Rohan, to separate it from the State of Rohan in the U.S.G.
I really haven't thought about this
Also, for future reference, I prefer she/her pronouns... (That's the personal thing I was discussing)