Yuan (媛) in Chinese means "beautiful woman." Yuan (源) is "source" or "origin." Yuán (缘) is "fate-connection" — the karmic threads connecting destined people. Multiple characters give the same sound.
Yuan is widely used in China.
Yuan does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
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In Pythagorean numerology the letters of Yuan reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.