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Tolkien based a lot of his names, especially the elvish ones from Welsh. There is a Welsh name Anwen, meaning very beautiful. It fits Arwen

According to this site, yes...

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If you click on the link for Arwen, you'll see that it was invented by Tolkien. If you click on Eowyn, you'll see that it was also invented by Tolkien, but was derived from old English.