Yeah, that's the thing -- I'm not used to it at all (context: I'm Chinese Singaporean), and doing 'given-family' for East Asian skaters -- though perhaps not for Japanese skaters -- just seems unbearably odd, and has the added bonus of making me feel weirdly defensive about it. I assume (with the added caveat that I may be wrong) that Yuna, having spent the larger part of her life in Korea, would be most accustomed to thinking of herself as 'Kim Yuna' instead. Like I said, it's different for the Japanese -- they seem to be more used to the given-family order, and as kyasuriin pointed out, may actually prefer that.

Given that it's fic we're talking about, if (say) Yuna were the pov character, having her refer to herself as 'Yuna Kim' would be pretty jarring for me.