Yui makes more sense to me than Ewey in written form, since Yui is a Japanese name. Ewey would be more along the lines of how to properly pronounce Yui. Also, it appears that the term Yui is a girls name and appears to mean Elegant Cloth, as well as alone, which would be rather relevant to this character's abilities.
https://en.wikipedia.org/wiki/Yui_(name) also other google searches.