My parents told me that when they were naming me, they researched to see if Éowyn was pronounced AY-oh-wihn, or EE-oh-wihn. They decided it was the former, but that doesn't mean they were right. I was always under the impression that Tolkien wanted for "e" to be pronounced "ay" but I could be mistaken. I know my name for one is pronounced "AY-oh-win"!