In terms of his relationship with Kakashi and the other Konoha senseis, it would be complicated. They might feel disappointed in Naruto. But with Konan, Naruto would be in a new environment where they share the goal of building up Amegakure. Naruto would have to adapt to Konan's leadership style, and they would have to communicate well to make things work in the village. His relationship with the other villages' shinobi would also change, as they would view him as an Amegakure shinobi now and might be more cautious or even hostile towards him.
Naruto's relationship with his old friends in Konoha would be strained. They may not understand his decision to join Amegakure. However, with Konan, he would build a unique relationship. Konan could become like a mentor and a friend to Naruto in Amegakure. She could introduce him to the culture and the people of Amegakure, and they would rely on each other in times of trouble. Also, Naruto might have to deal with the distrust of some Amegakure shinobi at first, but gradually earn their respect and form new relationships.
His relationship with Sasuke would be greatly affected. Sasuke might see Naruto's move as a betrayal to Konoha and their bond. On the other hand, Naruto's relationship with Konan would become very strong as they are now comrades in Amegakure. He might also form new friendships with the shinobi of Amegakure who would look up to him for his power and his new ideas for the village.
In this fanfic, it could be that Naruto is on a mission to bridge the gap between the major villages and the smaller ones like Amegakure. He teams up with Konan as she has a deep connection to Amegakure. Naruto's presence in Amegakure could attract other powerful shinobi to join them. They could then form an alliance within Amegakure that is based on equality and mutual respect, and start to change the perception of Amegakure in the shinobi world.
His relationships with his old friends in the Hidden Leaf would become extremely strained. They would see him as a traitor. For example, Sakura might be heartbroken and angry at him. Kakashi would be disappointed. However, within Akatsuki, he could form new relationships. He might become friends with some of the members who have a similar background of being misunderstood. For instance, he could bond with Hidan over their strong beliefs, though their beliefs are very different in nature.
Naruto's outgoing personality would have a big impact. Amegakure is a rather somber place, and Naruto's cheerfulness could start to lighten the mood. His ability to see the good in people might change how the Amegakure ninja view themselves and others. For instance, he could encourage those who have been involved in darker deeds to seek redemption.
His relationship with Sasuke would become more complex. Since they are from different villages now, there would be a new dynamic. Sasuke might see Naruto's move as a betrayal to Konoha at first. But Naruto's intention could be to bridge the gap between the two villages for Sasuke's sake too.
His relationships would become more complex. He'd have to start from scratch with new people. Some might be friendly right away, while others could be hostile.
His relationship with Sasuke would become even more complex. Sasuke might see Naruto's joining of Akatsuki as a betrayal or a sign that Naruto has finally given up on Konoha. Naruto's old friends in Konoha, like Sakura and Kakashi, would be very confused and hurt. They might try to bring him back, but also be wary of his new Akatsuki ties. And within Akatsuki, Naruto would have to navigate relationships with members who have different motives and personalities, some of whom might not trust him at all.
His relationship with Sasuke would be interesting. Sasuke might be initially suspicious of Naruto's decision to join such a secretive group. But Naruto could convince Sasuke that he's doing it for the greater good of the village and the ninja world, and they could end up working together on some behind - the - scenes missions.
If Naruto is banished to Suna, his relationships will shift significantly. In Konoha, he had friends like Sakura and Shikamaru. But in Suna, he'll be starting from scratch. With Gaara, their relationship could deepen as they both understand the pain of loneliness. Naruto could also become a mentor - like figure to some of the younger Suna ninjas. His relationship with the Suna elders might be a bit tricky at first, as they would need to trust him, but over time, it could grow into respect and mutual cooperation.
He could meet Konan. Since Konan is an important figure in Amegakure, Naruto might have some interesting interactions with her. They could exchange ideas about peace and the future of the ninja world.
In the 'naruto joins amegakure fanfic', Naruto would probably face some challenges at first. The people of Amegakure might be suspicious of him. But he would gradually win them over with his determination and kindness. He could also introduce new forms of chakra control to the local ninjas, which would enhance their combat abilities.