Yuki Kuran and Kaname Kuran have a long history and a complex, if somewhat at times, mysterious relationship.
Background
Kaname once declared that Yuki was born to become his wife. As a child, Yuki adored her older brother and the two shared a relatively close relationship. Due to fears over her safety, Yuki's birth was kept secret from the rest of the vampire society, and for the first five years of her life, she was kept hidden in the basement of the Kuran mansion from the outside world with only her parents and older brother as companions.
Yuki's parents managed to keep their daughter safe until the night Rido Kuran attacked the Kuran household, murdering Haruka in the process, and spurring Juri into sacrificing her own life in a final attempt to protect Yuki by transforming her into a human. After severely injuring Rido (though unable to land the killing blow), Kaname took the unconscious Yuki to the home of Kaien Cross, a former Vampire Hunter and longtime friend of the Kurans. Upon awakening, Yuki no longer remembered the first five years of her life, instead with her first human memory was of Kaname saving her from a vicious level E vampire.
Yuki then spends the next 10 years of her life living as Kaien's adopted daughter while Kaname is taken in by the Ichijo family under the watchful eyes of the vampire council.
During this ten year separation, Kaname is tricked by Kaien into visiting Yuki, opportunities which allow the two to grow close once again, and which gives Kaname a temporary respite from the vampire council. With Yuki, Kaname is able to laugh and relax and behave more like a normal human as he fondly watches over her. Kaname also makes it a point to visit Yuki each year on the anniversary of her being saved from the level - E, a day Yuki calls her birthday. The human Yuki grows trusting and fond of Kaname and holds a strong belief in his kindness based upon his gentle caring of her. She soon falls in love with Kaname and begins looking forward to each of his visits.
Despite their closeness in her early childhood years, Yuki and Kaname's relationship changes after the creation of Cross Academy. Knowing Kaname is living nearby in the school's dormitories, Yuki decides to pay him a visit. Unable to locate him, she falls asleep on the dormitory stairs while waiting for him. Kaname finds her soon afterward nearly gives into the temptation of drinking her blood. Kaname then takes Yuki to his bedroom and proceeds to drink Ruka's blood in an attempt to quell his hunger. Yuki awakens from her slumber in the guest bedroom while Kaname is still drinking Ruka's blood, the scene causing her to run away in shock and fear. Finally having come to understand that vampires and humans truly are different from one another, Yuki's relationship with Kaname becomes more distant than it once had been, to the sadness of both.
Summary
Prior to Yuki's Awakening
At the beginning of the series, Yuki is 15 years-old and a first-year student in the Day Class at Cross Academy, where she also acts as a school Prefect/Guardian. As the Night Class president, Kaname is one of the most popular and influential students at Cross Academy, and seemingly unreachable for a normal girl like Yuki. However, the Night Class share a secret which only the school Prefects, Yuki and Zero Kiryu know: they are all vampires, and Yuki and Kaname also share a secret past of their own: Kaname once saved Yuki from a vampire when she was 5 years-old. Due to this, Yuki regards Kaname as her savior and the two enjoy a special bond. Kaname calls Yuki his "dear girl" and Yuki quietly returns his affections, though she often feels awkward and inferior around Kaname due to his status as a respected Pureblood vampire. She also showed a bit of her insecurity when Sara Shirabuki was first introduced at a party held by the Aido believing that the Pureblood vampiress is perfect for Kaname, completely unaware of what she truly is.
Although Yuki states that she is in love with Kaname, she finds his attachment and his gentleness toward her confusing, often contemplating it as a dream and not reality. This would often lead to her assumptions of being treated as a kid, which she doesn't like, especially when it is done by Kaname. On the other hand, Kaname spends much of the first arc working to protect Yuki, which includes killing Shizuka Hio and fostering Zero's powers to defeat Rido Kuran when the Pureblood comes for Yuki.
During the climax of the Rido Kuran Arc, Kaname bites her, reawakening Yuki's vampire side and returning the lost memories of the first five years of her life. Yuki is initially disturbed upon her awakening at the thought of being in love with her brother, however Kaname reminds her that they are engaged and that intermarrying is a common practice among Pureblood vampires as their father and mother were also siblings.
Kaname suggests he and Yuki leave Cross Academy in order to escape from Rido, a plan Yuki refuses out of a sense of duty as a school prefect and a need to protect her friends, and on the basis that she couldn't forgive herself if she ran away. Kaname is upset at her refusal; however, Yuki kisses him and promises to return to him afterwards. Yuki keeps to her word, and after the fight with Rido ends, she parts with Zero and returns with Kaname to their family home. Kaname finally confesses all that he has done to protect her, including using Zero's bond with Yuki. Yuki is initially upset, though accepts his sins and wishes to share the responsibility for his actions done on her behalf, believing that she was the one who had propelled Kaname to do such dreadful things. It is also when she had finally realized why Kaname always looked so sad when gazing at her during her years as a human.
Kaname also murders the corrupt vampire council, an act which sends the vampire society into disarray and earns him a number of enemies. He spends the year following Rido's attack reorganizing vampire society and maintaining peace between humans and vampires. Afraid for Yuki's safety, Kaname has her remain inside the Kuran mansion during this time and limits her contact with the outside world requesting that Yuki neither communicate nor have visitors at the mansion.
During this time, Yuki returns to calling Kaname "brother (formally)" and occasionally "Senior Kaname" despite his repeated requests to simply call him "Kaname." In addition, she experiences some difficulties relearning how to use her fangs and seems to be in a perpetual state of bloodlust and hunger, desperate for Kaname's blood. Although Kaname regularly gives her his blood, Yuki reveals that without Zero's blood, Kaname cannot satisfy her hunger; and in spite of this she asks to remain by his side. Kaname accepts her request and returns Artemis to her stating that he would rather be killed by her than be apart.
Following the return of Artemis, Yuki leaves the house and gets into trouble after being attacked by another Pureblood vampire, Toma, whom Kaname severely punishes for hurting Yuki. Kaname reveals that he deeply fears losing her as this has happened to him before.
Kaname the ancestor
After finally telling Yuki that he is not her real brother, Yuki drinks Kaname's blood and is swept up in his memories, witnessing Kaname's reawakening by Rido, which included the murder of her true brother, and Kaname's distant past as the ancestor who saw the rise of vampires. As one of the progenitors of vampires, Kaname fought to ensure humanity's survival, following the Hooded Woman, another vampire who organized the Pureblood vampires, protected the humans, and later created the Vampire Hunters and Anti Vampire weapons. As his friend, mentor, and possibly lover, the Hooded Woman's death left a deep impression upon Kaname, prompting Yuki to ask Kaname if the Hooded Woman could ever be replaced. However, Kaname assures her that no one is ever a replacement for another. Years after the deaths of all his companions, Kaname eventually falls into a deep depression and lies down in his coffin, intending to sleep forever now that he had been left as the last of the ancestors.
After awakening from Kaname's memories, Kaname seeks confirmation from Yuki that she understands he is not her brother. Yuki declares that she will call Kaname by his name from then on, rather than "brother (formally)" as she had been, as she realizes that he is fragile. Nagamichi Aido who is visiting with Kaname, asks Yuki if she would be able to stop Kaname if she disagreed with his actions. Yuki declares that she can't do anything until she is Kaname's equal and mulls over the distance between them.
Kaname faces Yuki and asks what she thinks of him, she responds that she knew him as her brother, her senpai, and now he is her ancestor. She also states that Kaname is a beautiful man, but is a beast like her, he is a bit fragile, lies, is dodgy and a liar, and has too many secrets. She feels uncertain of his feelings for her, but amends that he loves her, however there are other things mixed up in his feelings for her. Ultimately her best answer to his question is to ask if they can start over and she can watch him properly, to which he hugs her tightly and agrees. Yuki is happy that she has finally faced him as an equal and they can start over.
Separation
After saying goodbye to Yuki, Kaname leaves saying that he has very important duties to attend to, Yuki troubled, begs him not to leave. Kaname asks her to look after the hous\\e and tells her not to hesitate, before leaving the house. Yuki runs out of the mansion in search of Kaname and she runs into Kaien and Hanabusa. Following her sensing of Kaname, Yuki directs them to the Hanadagi Castle and they arrive to witness Kaname murdering Hanabusa's father. Kaname turns to Yuki and advises her that he can no longer hesitate and is returning to his original plan. He apologies and thanks Yuki before disappearing. After Yuki unfreezes from her shock, she chases after Kaname in a desperate almost crazed state, unable to believe what has occurred when they just promised to start all over again.
Yuki gets taken to the Vampire Hunter's headquarters for questioning, but she knows nothing about Kaname's intentions. Yuki vows to take Kaname's place and keep the peace between vampires and humans, but she demands to be the one to confront Kaname. Yuki sets up the Night Class and continues to promise Aido that she would go after Kaname, but continues to delay until things are more stable. Yuki hears about Kaname killing more Purebloods, she refuses to accept it and mentally begs for Kaname to stop. The hunters declare they have no intention of stopping Kaname, but Yuki tells Zero that she wants to stop Kaname.
Kaname clashes with Kaien when he feigns an attack on Isaya and asks Kaien to tell Yuki that he killed Ouri and that Sara is next. Kaname arrives at the school and Yuki tries to go to him before she realizes he has not come to take her away. Kaname reiterates that she is a hindrance to his plans crushing Yuki. He tells Zero and Yuki that he released Shizuka from her cage because he wished her to attack a certain hunter couple and leaves as Yuki cries about everything. Yuki comes to the realization that she is the source of everything and becomes determined to stop Kaname.
Their Relationship
Due to Yuki's widely changing circumstances, the nature of Yuki and Kaname's relationship has gone through many changes.
Yuki as a Human
Often uncertain of Kaname's feelings for her, Yuki claims he sees her as nothing more than a pet, despite the fact that Kaname often refers to her as "his dear girl." During their separation, Kaname often appears lonely, and Yuki observes that besides herself, few people are close to him.
As a child, Yuki always referred to Kaname as her "Onii-sama" (a respectful and formal Japanese term for elder cousin or brother), while after turning human, Yuki at first called him "Kaname" (informal), but after their relationship became distant she began referring to him as "Kaname-sama" (respectful and formal), and "Kaname-senpai" (respectful address for an older student) while at school. Yuki revealed in 25th Night that she had been determined not to refer to Kaname as "Kaname-sama" in a deliberate attempt to distance herself from Kaname, but still accidentally finds herself using it.
After Yuki's Awakening
Following her reawakening, Yuki returns to calling Kaname "Onii-sama" and occasionally "Kaname-senpai," despite his repeated requests to simply call him "Kaname." During this time, Yuki and Kaname
Yuki Kuran and Kaname Kuran
appear to be affectionate with one another and share occasional kisses; however, it's later revealed that Yuki continues to feel inferior to Kaname, making her unable to address him informally and preventing their relationship from progressing forward.
In spite of her feelings of inequality, when asked by Kaname how she sees him after revealing his past to her, Yuki responds that she thinks he keeps too many secrets, is a liar, and is somewhat vicious. Yuki suggests that they start over, so that she can get to know the real Kaname. Unfortunately, this does not lead to many answers as Kaname leaves Yuki shortly after this, determined to carry out the plan he had formed prior his revival. Kaname's own feelings on the status of his relationship with Yuki are extremely ambiguous, but prior to enacting his plan, he had indicated that he still wished to return to Yuki.
The conclusion can be drawn that Kaname's deems his plan to be more important than his relationship with Yuki, though it is obvious that he is also doing this for Yuki, in spite of the fact that she may not approve his methods.
She fights Kaname with her Artemis and he uses his sword, and Yuki wonders if killing the Purebloods was "her" wish - her being the Hooded Woman who sacrificed herself to create the Vampire Hunters and Anti Vampire weapons.
Kaname and Yuki are reunited, Kaname feeling guilty over leaving her. Even after he insists that he will not leave her, again, she refuses to let him go, calling him a "LIAR", and telling him that every memory she had of him since he rescued her from the Level-E Vampire (the night her memories were erased by her mother, Juri) were all lies. Kaname proves his devotion to Yuki by taking her back to their room in the house she was born in and making love to her.
Two months after Kaname was encased, it is revealed that Yuki had not left his side since. After she nearly attacks Yori due to blood-lust, she finds afterwards that she is pregnant with Kaname's daughter and resolves to live, for him and their child.
Later on, Yuki dreams about Kaname holding their daughter and says how wonderful it would be if that had happened.