If I were to call a son/ daughter something from lotr it would be because of what it means rather than being a character. For example, Aragorn. I would name my son this, because it means 'white tree', not because Aragorn is a very popular lotr character. I doubt I would call my daughter something from lotr, but if I did, she would be called Eowyn. But I already picked Opal, because it's my birthstone.
