If Kakashi goes back in time, his relationship with Rin would be complex. He might try to protect her more, which could lead to a different dynamic between them. He would be more aware of the threats she faces and could be more proactive in her safety. With Guy, he could be a better friend from the start. He could join Guy in his challenges and competitions more often, strengthening their rivalry - friendship. And when it comes to the Third Hokage, Kakashi could offer more insights based on his future knowledge. This might make the Third Hokage rely on him more, and Kakashi could become a more important figure in the village at an earlier stage.
With Minato, Kakashi's relationship could also shift. If Sakumo is alive, Kakashi may not be as eager to prove himself in the same way. Minato might see a different side of Kakashi, one that is more at peace with himself. This could lead to a more mentor - mentee relationship based on mutual respect and understanding rather than Kakashi's need for validation.
Well, for Naruto and Sasuke, their relationship might become even stronger earlier. In the past, they could train together more and understand each other's pain from the start. Sakura might be more assertive in her relationship with Sasuke, as she has the knowledge of what will happen in the future. She could try to prevent Sasuke from going down a dark path right from the beginning. And among the other members of Konoha 12, they might form closer bonds as they rely on each other more in this strange new situation of being in the past.
Their relationships would likely become stronger. They would have to rely on each other more in the unfamiliar past environment. For example, Naruto might look up to Kakashi even more as he sees how much Kakashi has grown and changed. Sasuke might be more open to the idea of teamwork as they face challenges together in the past.
Since Naruto has more knowledge of the future, Kakashi might start to rely on him more, which could shift their relationship. Naruto could also see a different side of Kakashi from the past, and this new understanding could deepen their connection. For example, they might have to face some challenges together that make them trust each other more than before.
His relationship with his father, Ned Stark, would be different. He could finally have a real father - son relationship instead of the hidden one. He might be able to learn from Ned and become an even better leader in the North.
His relationship with Katara would be very different. He might be able to approach her in a more confident way, knowing what they've been through in the future. He could also avoid some of the misunderstandings that happened between them in the original timeline.
With his Slytherin peers, Draco's relationship would shift. He might encourage them to be more inclusive and less focused on pure - blood supremacy. This could make him an outcast among some of the more traditional Slytherins, but also gain him new allies who are open to change.
His relationship with Kakashi would also change. Naruto could use his Rinnegan - enhanced knowledge to help Kakashi deal with his past traumas earlier. He might also show Kakashi new jutsu or ways of combat that he learned in the future. This would make Kakashi see Naruto in a whole new light and their bond could become more of a teacher - student relationship in reverse.
Regarding his relationships with his friends and comrades, like Samwell Tarly, things would be altered. He might not meet Sam in the same way as before. And his relationship with Daenerys Targaryen could be completely different. Instead of meeting her during the events of the original story, he could meet her when she was much younger, and this could lead to a very different kind of relationship, maybe one that's more of a mentorship or a completely different romantic connection.
Link's relationship with his own past self could be a really interesting aspect. If he meets his younger self, there could be a sense of mentoring or even confusion. His younger self might not understand what's going on at first. And when it comes to friends like the Koroks, if he goes back to a time when the Korok Forest was in a different state, their interactions would be new and different. The overall web of relationships would be completely reshaped as he steps into a different time period in Hyrule's history.