When it comes to the other Konoha 11 members, Naruto's relationships would be altered. For instance, with Shikamaru, instead of just being comrades, they could have a more complex relationship. Shikamaru might be more cautious around Naruto because of his new family status. And Naruto's bond with Hinata would be different too. Hinata might be more intimidated by Naruto's new identity as Kushina's brother, which could change the way their relationship develops over time.
With Sakura, Naruto's relationship could change significantly. In the original, Naruto had a bit of a crush on her. But as Kushina's brother, he might see her more as a friend or even a sister - like figure. And his relationship with Kakashi would also be different. Kakashi might respect Naruto more because of his Uzumaki heritage from the start, rather than gradually as in the original story. He could also expect more from Naruto due to his stronger family ties in the village.
His relationship with Minato would be very different. Instead of a father - son bond, it would be more of a brother - in - law type of relationship. Minato might see Naruto as an equal in a different way, and they could collaborate more as peers. Also, Naruto's relationship with Sasuke would have a new angle. Sasuke might be more envious of Naruto's strong Uzumaki bloodline, which could intensify their rivalry.
Naruto's relationship with the other Jinchuriki would likely change. If Naruto hates Yondaime, he might see the system of creating Jinchuriki in a more negative light. He could try to convince the other Jinchuriki that they have been wronged by the villages and their leaders like Yondaime. This could lead to either a united front among the Jinchuriki against the villages or some internal conflict among them depending on their individual beliefs.
His relationship with Sasuke could change. Since Kushina was very protective, Naruto might be even more over - protective of Sasuke. He would not let Sasuke take any unnecessary risks and would always be there to support him, which could either annoy Sasuke or make him appreciate Naruto more.
His relationship with the Hokage at the time, say Tsunade, would change significantly. Tsunade might involve Naruto more in important village decisions, seeing him as a link to the village's founding. Also, Naruto's relationship with the Uchiha clan could be different. They might be more wary of him, or on the other hand, see him as a potential bridge between them and the Senju due to his relation to Hashirama.
His relationship with Sasuke would likely be very different. Since Sasuke has also had experiences with the Rinnegan, they might now have a new level of understanding between them. They could train together to master the powers of the Rinnegan or compare notes on how to use its abilities.
Well, Naruto's relationship with his male friends would take on a new dynamic. For example, Shikamaru might be less dismissive of 'male' Naruto as he might expect different behavior from a boy. Naruto could also get closer to some of the more reserved male characters who usually keep their distance from girls. On the other hand, his relationship with female characters like Ino could become more complex. Ino might be intrigued by this new 'boy' in town and try to figure out what makes him different. And Naruto would have to constantly balance his real self and his pretend self in all these relationships.
With Kakashi, Naruto's relationship would also shift. Kakashi has had experience with the Sharingan and knows about powerful dojutsu. He would be both amazed and a bit worried about Naruto having the Rinnegan. He might try to mentor Naruto more intensively to make sure he uses it for good and doesn't let the power corrupt him. Naruto would look up to Kakashi even more as he tries to learn about his new power from Kakashi's knowledge.
His relationship with Jiraiya would be different. Jiraiya trained Minato, but with Naruto replacing Minato, Jiraiya might train Naruto even more intensively from an earlier age. Naruto would also probably be more open with Jiraiya about his feelings and plans, as he's not as reserved as Minato.
His relationship with Sasuke would be extremely complex. Sasuke, who has his own vendetta against the shinobi world, might initially be suspicious of Naruto's new role. But Naruto, as the Akatsuki leader, would try to convince Sasuke to join him in his new vision for the organization. It could be a love - hate relationship where they constantly butt heads but also understand each other on a deeper level.
His relationship with Sasuke would be very different. Instead of being rivals, they might become more like comrades or even brothers in arms, as Itachi and Sasuke were related. Naruto would probably be more understanding of Sasuke's thirst for power and revenge, and might try to guide him in a more Itachi - like way. With Sakura, Naruto might become more distant, as Itachi was not very close to female characters in the original story. And with his other friends like Shikamaru or Kiba, Naruto would likely be more reserved and less of the loud, exuberant self they knew, which could cause some confusion and concern among them.
When it comes to his friends like Shikamaru and Choji, Naruto might distance himself from them. Zabuza is a loner, and being raised by him, Naruto could start to prefer solitude. He might not value the group dynamic as much as he does in the original story and instead focus on his own strength and survival skills.