Ken Kaneki has undergone significant transformation since Tokyo Ghoul first began. Most people remember Kaneki's first significant alteration, when his demeanor completely altered and his hair became white as a result of being tormented. But that's not the only change he's undergone.
Every significant incident in the tragic hero's life causes Kaneki's worldview and physical appearance to change to match his new normal. It's possible to further dissect the patient Kaneki, but most admirers concur that he has six unique personas. It wouldn't be a leap to think of these Kens as wholly distinct individuals - in fact, one of them is - ranging from calm and lovely to vicious and psychotic. Here is a description of each Kaneki form, along with information about how they function in the series.
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Kaneki 1 Has Black Hair, Is Shy & Bookish
The first Kaneki is a shy, bookish college student who becomes a Half-Ghoul after a date goes horribly wrong. Luckily, he finds a place in the Ghoul-friendly coffee shop Anteiku, where he works as a server and learns about the Ghoul community. As an idealist, this Kaneki is deeply troubled by an unjust world, and struggles to make sense of why Ghouls exist at all. Much later in the series, we learn that this Kaneki was withholding some pre-Ghoul trauma - after losing his father, he was frequently abused by his mother, leading to severely low self-esteem. As a survival tactic, Black Hair Kaneki adopted the mindset of it being better to be hurt himself than to risk hurting others, though this lead to a weakness that he himself could hardly stand.
The iconic version of Kaneki 2 has white hair.
It's after being tortured that Kaneki undergoes his most iconic shift, accepting himself as a Ghoul as his hair turns white. There are a few theories as to why his hair suddenly changed color. A popular one is that it's due to Marie-Antoinette Syndrome, a real-life condition connecting white hair and trauma. Another involves his awakening as a Ghoul boosting his count of the fictional "RC cells." Regardless, the change was a symbolic for Kaneki's change as a person. White Hair Kaneki rejects his past self, deciding strength is everything and all suffering is caused by one's lack of ability. Now cold, harsh and very powerful, Kaneki still wants to protect those close to him, but he pushes them away in doing so. As it turns out, this philosophy is his ultimate downfall. Anteiku is destroyed and Kaneki is cut down by Kishou Arima.
Kaneki 3 Is the Traumatized Centipede
Centipede Kaneki emerges in Kaneki's Half-Kakuja form, a powerful Ghoul transformation enabled by cannibalization. Centipede Kaneki completely loses his grip in this form, mumbling incomprehensibly, deliriously running up walls and impaling foes with centipede tentacles. It is a manifestation of Kaneki's torture, referencing the centipedes Jason would insert into his ear canal. When Kaneki's personalities gather in Tokyo Ghoul: re Chapter 141, this Kaneki was not present, indicating it may be more of an extension of White Kaneki than its own person. Prisoner #240 (who was present) is more or less the same -- a mumbling, psychotic identity formed from Kaneki's traumatic experiences.
Kaneki 4 Is Actually Haise Sasaki
Haise Sasaki isn't really Kaneki at all. After "dying" at Arima's hand, he is degraded to the nameless Prisoner #240 and revived as an amnesiac. Tortured and ashamed, he wants to forget everything that's happened to him. Captaining the Quinx Squad of the CCG, Sasaki is able to do just this, and he lives happily for a brief period as the kind, caring and somewhat awkward "den mother" of the Quinx. Of course, Kaneki's history comes knocking in the form of a hallucinated child Kaneki, who begs Sasaki not to erase the past. When Kaneki's memories return properly, he says, in one of the series' most memorable quotes, "Goodnight, Haise. I've had enough of dreaming."
Kaneki 5 Is the Darkest Personality, Known as the Black Reaper
The Black Reaper is the darkest Kaneki in the series. Similar to White Kaneki, he is cruel, cold and merciless, recalling everything that has happened to him and refusing to accept Sasaki's momentary happiness. He remembers it all - the torture, the failure and even his childhood abuse. Similar to how White Kaneki deserts Anteiku, the Black Reaper deserts the Quinx squad. He even scolds Urie for not preventing Shirazu's death. He's definitely a lot bleaker than White Hair Kaneki, as he is explicitly suicidal. When he once again confronts the "White Reaper" Arima, he is fully prepared to die.
Kaneki 6 Is Tokyo Ghoul's Complex One-Eyed King
The One-Eyed King is perhaps Kaneki's most complex personality. Following his fight with Arima, Kaneki regains the will to live and becomes the One-Eyed King. His previous personalities converge into a reformed, complete Kaneki who knows what's important and is ready to carry on Arima's will. His hair once again turns white, marking what seems to be a positive shift for his character. It's certainly an improvement, but the old shortcomings still hinder the tragic hero.
He shoulders too much responsibility, spiraling out of control as the stress causes him to age. He ultimately fails once more, cut down by Juuzou Suzuya and transforming into the "Dragon" Kagune monster. In a more subtle change, Kaneki's visions inside Dragon help him make sense of his himself and come to terms with the world. He learns to rely on others and understands that the world is not wrong - it just is. It is this content, existentialist Kaneki that ends the series.