According to Naoto's winquote against Terumi, he's got a presence of someone who is associated with the Terumi clan. The Terumi clan's leader has the Hunter's Eye - a special ability in their right eye that allows them to see the life force values. After Saya Terumi killed all of her clan except for Naoto, Naoto was selected by the Hunter's Eye as the head of the clan. When Saya tried to kill Naoto in the second novel, she said that she'll take his eye.
Terumi, in his ghost form, doesn't have a right eye. And "yūki" means "ghost". But, according to Mori, Terumi's name is not his real name. But what if Mori was talking only about the "ghost" name?