You know what I always wonder about? The fate of Master Lio.
All the world leaders and their staff know Kavik as Lio. And it's not like he was just a faceless staffer at a meeting - he was the sole (public) companion of the Avatar at THE global political meeting of the year. The rumor mill was going wild about the two of them. "Lio" interrupted the meeting, and then emptied out Iwashi's coffers in a game of sparrow bones. Surely all the Zhongdus, heads of state, ambitious earth sages, etc. and their staff know about him, at least by name if not face.
On the other hand, Kavik can't be Master Lio forever. There are people who know him as Kavik - the thinclaws, for one. The Bin Er waterbender community for another. Also Kavik's parents, who are so proud of their baby boy for serving with the Avatar
I feel like there's no winning for them now - if they admit Master Lio was an invented identity, it reveals that Yangchen is playing the game, partaking in politics and deception, and also undermines the "It was spirits that blew up the city" story. But if they don't do that, Kavik has to live under a false identity forever, and people will be forever pulling aside Yangchen to let her know her companion isn't who she thinks lol
IDK, maybe I'm overthinking it, and Kavik can just wear a funny hat and say Lio is his cousin who works by the docks.