Throughout arc one, Zero and Kaname have had an antagonistic relationship, allies only for the sake of Yuki Kuran. This relationship does not seem to improve much as the story moves into arc two.
Zero Kiryu possesses complete distrust of Kaname Kuran's motives, even going so far as to beg Kaien Cross not to trust him. At their first meeting, Zero attempts to stab him upon sensing that Kaname is a Pureblood vampire. Part of their mutual dislike of one another stems from their shared feelings for Yuki, with Zero becoming jealous of Yuki's affection for Kaname almost immediately, and Kaname's jealousy of Zero following soon after upon witnessing Yuki's concern over Zero. While Zero typically speaks to Kaname in a rude manner, Kaname often never misses an opportunity to taunt Zero in return.
The start of the storyAware that Zero was bitten by a Pureblood vampire, Kaname expresses concern over Zero's inevitable awakening as a vampire and asks Kaien Cross to move him to the Night Class. Despite his misgivings over Zero's condition, Kaname expresses respect for Zero's strength of will to resist the vampire instincts for four years.
After Zero's full awakening
Kaname expresses great disgust for Zero succumbing to his vampire nature and biting Yuki. Kaname gets very angry that Yuki is reminded of the first vampire she saw him kill. He also gets irritated by the fact that "his precious girl has been bitten by another". Kaname however quickly regains his composure and repeatedly reminds Zero that he owes Yuki for what she has done for him.Kaname has already decided that Zero is his tool to protect Yuki. He advises Zero that despite his anger over his drinking Yuki's blood, he is allowing him to live and be Yuki's shield. When Shizuka Hio as Maria Kurenai endangers Zero, Kaname only expresses a little regret for the loss of his tool, believing Zero expendable. When Zero was struggling to fight against his Level E instincts and was subsequently locked up in an underground cellar by his teacher Toga Yagari, Kaname soon appeared and forced Zero to drink his blood, which he claimed would heal him slightly, as it was the blood of a Pureblood. Kaname also harshly stated that this was for Yuki.
Zero figures out that Kaname was the one who killed Shizuka after he gets confused over Kaname saving him from the council's vampires. He confronts Kaname to find out why the Pureblood killed Shizuka and is surprised that Kaname wanted him to drink Shizuka's blood and even expresses envy that Zero is able to protect Yuki. Zero chooses not to reveal the truth about Kaname. At the very last moment, Kaname taunts Zero with the fact that since his blood was "inside" Zero, it is really in fact "him" protecting Yuki, not Zero. Overall, Zero's civility has increased towards Kaname, though it always borders on rudeness.
Kaname's jealousy of Yuki's attachment to Zero causes him to be ruder to Zero and go as far as naming him a suspect when a human girl is being bitten at Cross Academy. Though Zero denies it, Yuki is more offended by it than Zero is. Despite Kaname's accusation, he fully trusts Zero to protect Yuki to the best of his ability, reminding Zero of this on multiple occasions.When Kaname convinces Zero to bite him, he expresses his most honest thoughts. Kaname tells Zero he hates him and causing Zero to shoot at the side of his head. Kaname slashes Zero's neck and he reveals how often he has thought about killing Zero with a single blow, but does not want to release Zero from his suffering. Zero only submits to taking Kaname's blood in order to stop hurting Yuki.
After Yuki becomes a vampire
Zero's anger toward Kaname is back stronger than ever. Compiled with all of his issues regarding Purebloods, Kaname is his foremost living enemy now. The two attack each other after Rido Kuran was killed, but he said that he wants to kill Yuki as well. Kaname gets mad because Zero pointed his gun at Yuki.
After the year
Zero spent the year after Rido's attack trying to track down Kaname. Zero held him responsible for the chaos that followed after the destruction of the council, but Kaname proved to be elusive. When Kaien tells Zero that Kaname has become the head of vampire society, Zero relents in his hunt, agreeing that Kaname is needed to keep the vampires in line. The two characters have little contact for most of the second arc until the end, when Kaname attacks Vampire Hunter headquarters in an effort to free the Hooded Woman from the furnace. During the attack, the trio meet up again near the Academy and Kaname reveals to a shocked Zero that he was the one who intentionally released Shizuka from her cage. As a rare Vampire Hunter twin, Kaname realized Zero would grow up to be a powerful Hunter, strong enough to defeat even Purebloods. However, in order to turn Zero into a weapon, Kaname also realized Zero would also need a deep hatred of vampires, a deep hatred that could only come from witnessing the deaths of his parents. Kaname leaves after confessing the truth, preventing Yuki and Zero from following. In the end, after Kaname resolves to become the new parent metal, he and Zero briefly set aside their differences and fight together to protect the Academy from the Purebloods' attack. Afterward, Kaname tosses his heart in the furnace to repent for his sins; however, in his final moments he embraces both Yuki and Zero, and urges them to be together.