Her real name is indeed (SPOILER)Sarah. I just played that part and I remember that well. Her father had wrote it to the eidolon wall.
By the way, does anyone know what happened to him (Garnet/(SPOILER)Sarah´s father) after that storm? Apparently he survived but what after that? And why Eiko was alone? Could she be close related to Garnet/(SPOILER)Sarah?
I don´t think that anyone in this game has lastnames. I haven´t noticed.