Eowyn (pronounced with a long "A" and a long "O", "A-O-win") means "horse lover" in Old English. This name was invented by J. R. R. Tolkien who used Old English to represent the language of the people of Rohan. In 'The Lord of the Rings' Eowyn is the niece of King Theoden of Rohan. She slays the Lord of the Nazgul in the Battle of the Pelennor Fields.
We chose the name both because we love Lord of the Rings, because we loved the sound of the name, and especially because we wanted Emma to be named for a strong female character whose story could perhaps one day inspire her own life.