The Hooded Woman

We do not know much about the Hooded Woman yet but, Kaname had an as yet undefined relationship with her in his past. It is suggested that she is the first woman with whom Kaname had a relationship after she recruited him to her side of the pureblood/founder war. The pair were possibly living together in 64th Night. Kaname had not wanted to fall in love or have any attachments for fear of turning his beastial hunger on that person, however she snuck in and created a small attachment.

Personality
She is more dominating than Kaname, more agressive, treating him in a submissive manner and the controlling person in their relationship. She has not yet been named.

"The first Vampire to die"
In the 63rd and 64th night she sacrificed herself as one of many an experiments she and Kaname were ongoing by throwing her heart into a furnace killing her and Kaname watches her shatter into glass before his eyes. Now her heart turned into stone, part of it is smelted in Hunter weapons, namely The bloody roses's bullets and Artemis. Before she dies she exclaims "It seems the only thing that can kill us, is ourselves". Kaname distressed about her death regrets that she was the sacrifice and wishes he had protected her.

Yuuki's Birth
When Yuuki is born in the manga, Kaname is seen talking to himself while carrying newborn Yuuki saying he recognises those warm eyes and says he will protect what is important to him this time. There seems to be some link between Yuuki and the hooded Woman.