Jung-won is the name of the female lead in this Korean drama.
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Literary in Chinese — you'll meet 贞媛 in classical poetry and old prose, not modern conversation. The Xinhua dictionary glosses it as 贞洁贤淑的妇女 'a chaste and virtuous woman'. Today the same characters most often appear as a Korean given name (정원 Jung-won) in K-drama subtitles.
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贞 'chaste/upright' + 媛 'beautiful/elegant lady' — both characters were valued in classical Confucian descriptions of women. 媛 (yuán) on its own appears in 名媛 (míngyuán, 'socialite'), preserving the old 'noble lady' sense.