Eiko - There a few derivatives for the name Eiko. Such as listed as it means "splendid child, long-lived child" and as well as "young landy". It is traditionally a female Japanese name and can also mean "variation in life".
Carol - Carol is seen as a female first name, but is used in this instance as a surname. It means "song, music" and is primarily female. It is quite linked to the songs of Christmas. It's origin is France.