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 could also feel a bit sad and lonely. He's used to being an outcast in the village, but he thought Team 7 would be different. So he might start to question himself. Maybe he'd start training on his own more, trying to become stronger so that they would have to notice him. And he might also try to find other friends outside of Team 7 to fill the void.
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.
He might feel very sad and lonely at first. Naruto has always craved family love and acceptance, so being ignored by them would be a huge blow.
Naruto might initially be very disappointed. He has always been eager to train and become stronger. So being denied by Kakashi could make him feel a bit down. But he could also be defiant. He might start training on his own, determined to show Kakashi that he doesn't need his approval to get stronger.
At first, Naruto would probably be extremely shocked and in denial. He has always looked up to Kakashi as a mentor and friend, so the idea of being betrayed by him would be hard to accept immediately.
Naruto might be initially very disappointed. He has always looked up to Kakashi as a strong and cool ninja, and being refused by him would be a big blow. He could become a bit sulky and withdrawn, feeling like he's not good enough.
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 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.
As time goes on, Naruto could become angry. He might feel betrayed by his family's lack of attention. This anger could fuel his determination to become stronger on his own, without relying on his family. He may start to train harder and focus on achieving his own goals, using the rejection as motivation.
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.