Well, Kakashi is a complex character. When he discovers Naruto is abused in the fanfiction, he may first feel a deep sense of guilt for not noticing earlier. He'd then use his skills and influence in the village. He could start by reporting it to the proper authorities in Konoha, like the Hokage. And at the same time, he'd be there for Naruto, providing emotional support, talking to him, and helping him through the trauma. Kakashi has his own past traumas, so he'd understand what Naruto is going through on some level.
Kakashi, being the responsible and caring person he is, would be devastated upon finding out Naruto is abused in the fanfiction. He would not tolerate such a thing in his village. His first reaction might be shock, but that would quickly turn into determination. He would use his Sharingan if necessary to figure out who the abuser is. He would also enlist the help of his friends and comrades, like Guy or the other members of Team 7. They would form a sort of protective circle around Naruto. Kakashi would also start training Naruto more intensively, not just to make him stronger physically, but also to build his confidence and self - esteem back up.
Kakashi might immediately offer a comforting presence. He could put his hand on Naruto's shoulder and just be there silently, letting Naruto know he's not alone.
Kakashi would likely be very concerned. He would immediately assess Naruto's injuries. If they were serious, he would use his medical skills to start treating him right away. His first reaction would be to make sure Naruto was stable and out of immediate danger.
He'd probably be a mix of angry and sad. Angry at whoever or whatever caused Naruto to be in this state, and sad because he cares about Naruto so much. He might clench his fists tightly, trying to control his emotions while he focuses on helping Naruto. He'd also feel a sense of guilt, wondering if he could have prevented this from happening.
He probably gets very worried. Kakashi is Naruto's teacher and mentor, so he'd likely be immediately concerned and rush to Naruto's side to assess the situation.
Kakashi's reaction would be complex. He is a man who has lost many people in his life. But Naruto was special. He would hold Naruto tightly, his hands trembling slightly. He might try to use some of his own chakra to keep Naruto alive a little longer, but deep down he knows it's futile. His face would show a mixture of pain, regret, and love. He would remember all the times he trained Naruto, all the lessons he taught him, and how Naruto had surpassed all expectations.
Kakashi might be initially shocked. After all, Naruto has always been his student and the sudden refusal to use the term'sensei' would be unexpected.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.
Eventually, Naruto could grow resentful. If the ignoring persists for a long time, he might start to think that Kakashi doesn't care about him at all. This could change Naruto's attitude towards Kakashi and might even make him more rebellious in his training or actions. However, deep down, he still probably hopes for Kakashi's recognition and approval.
Naruto would be devastated. He sees Kakashi as a mentor and father figure. He might initially go into denial, not believing that Kakashi would actually abandon him.
Kakashi would probably be very calm at first. He's an experienced ninja who has seen a lot. He'd gently pat Naruto on the back, offering silent comfort. Then he might start to speak softly, asking Naruto what's wrong in a gentle voice.