With Kakashi, Naruto's relationship could become more complex. Kakashi knew Minato well, so he would see a lot of Minato in Naruto. He might be even more protective of Naruto, but also have higher expectations. At the same time, Naruto might look at Kakashi as a connection to his father, seeking more guidance and approval from him than in the original story.
His relationship with Sasuke would be very different. Instead of just being rivals, they could be like brothers. Since Naruto would be related to Mikoto, Sasuke's mother, there would be a family bond between them. Naruto might feel more responsible for Sasuke's well - being and Sasuke could struggle with his feelings towards Naruto, as Naruto would now represent a part of his lost family.
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.
Naruto's relationship with the villagers could be affected. As he becomes a Minato fan, he would try to uphold Minato's legacy even more. The villagers, seeing Naruto's newfound admiration for Minato, might start to see Naruto in a new light, more like how they saw Minato. Also, his relationship with Hinata could be different. Naruto might start to model his family - centered values after Minato, which could bring him and Hinata even closer as they plan their own family.
His relationship with Sasuke would be very different. Sasuke, who has his own ties to Orochimaru, might see Naruto in a new light. They could either become closer due to their shared connection or more competitive as Sasuke might feel threatened by Naruto's new status. With Sakura, she might be more hesitant around Naruto. She has always seen Naruto as a friend, but the idea of him being related to Orochimaru could make her distrust him at first.
With Kakashi, Kakashi would be very cautious at first. He'd need to understand what this new development means for Naruto and the village. But as he sees Naruto trying to handle it responsibly, he would offer his guidance as he always has, but with an added layer of concern for the implications of Naruto's relation to Kronos.
His relationship with Sasuke would likely be different. Naruto's charm from Aphrodite might make Sasuke less hostile towards him initially. And his skills from Hephaestus could make Sasuke respect him more as a strong opponent. For example, if Naruto creates a really powerful weapon, Sasuke would see him as a worthy rival in a new light.
Harry's relationship with Dumbledore would also shift. Dumbledore would need to reevaluate his role in Harry's life. He might see Harry as a potential bridge between the wizarding world and the underworld, and try to guide Harry in using his new powers for good. At the same time, Dumbledore would have to be cautious as the underworld has its own set of rules and dangers.
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.
His relationship with his ninja friends would likely be strained at first. They might be confused or even a bit scared of his new powers. For example, Sasuke might see him as a greater threat now. But Naruto would try to convince them that he's still the same person. With his new divine family, he might have a rocky start too. Zeus could be a demanding father figure, and Naruto would have to stand up to him to protect his ninja way of life.
If they are revived, Naruto's relationship with his parents would be much more complex. He has grown up without them, and now he has to adjust to having them around. Minato and Kushina would also have to get used to the fact that Naruto is no longer the little boy they left behind. Their relationship would be filled with a mix of catching up and learning about each other all over again.
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.