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It can mean "moon" from the Japanese translation but according to Korean, it Yuna (or at least Yun, to my knowledge) can be translated to "allow, consent".
Kim Yuna's hangul name (according to wikipedia) would actually be translated to Kim Yeon-a but is written as Kim Yuna due to a mistake.
Yeona is usually meant as beautiful child so..I guess beautiful child is the usual translation