Translating directly, Yávien's name derives from yávë 'fruit' and the feminine ending -ien. So the entire name gives us the curious derivation of 'fruit daughter', though it is presumably not intended to be interpreted quite this literally. In Elvish, 'fruit' had the broader sense of 'fruits of the earth' or 'harvest' (the time of harvest being known as Yávië). So, one possibility is that Yávien was born at this time of year, and her name meant something like 'daughter of the harvest'.
It is also possible that Yávien's name was meant to evoke a dedication to Yavanna, the Vala known as the 'Giver of Fruits'. Yávien's father Nolondil named his second child Oromendil, clearly deriving from the Vala Oromë, so a similar connection to the Valar in Yávien's name seems entirely plausible.
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