The characters' relationships would be in upheaval. Naruto's friends in Konoha might feel betrayed or confused at first. His relationship with the other Kage would also be different. They might see him as a potential threat or an asset depending on their own village's interests. The relationship between Naruto and the Hidden Cloud's ninja would be a mix of suspicion and acceptance. Some would be proud to have him as the Raikage's son, while others would be jealous or think he doesn't deserve it. This would create a lot of drama and new storylines within the fanfiction.
If Naruto was the son of Raikage in a fanfiction, his relationship with Sasuke would be very different. Sasuke might view Naruto as having an even stronger connection to power and a village he despises (initially). This could add more fuel to their rivalry. On the other hand, Sakura might be more hesitant around Naruto, not sure how to deal with his new identity. And Naruto's relationship with his former sensei, Kakashi, would become a bit strained as Kakashi has to figure out how to handle Naruto's new ties to the Hidden Cloud Village.
The relationship between Naruto and the Raikage would be completely transformed. Instead of being just an ally or a foreign ninja, Naruto would be his son. This would likely lead to a more protective and perhaps more demanding relationship from the Raikage. Naruto's relationship with Killer Bee might also change. They could become more like brothers, with Bee helping Naruto to understand his new identity and the culture of the Hidden Cloud.
His relationships would change a great deal. He'd probably form a father - son type of bond with the Raikage. With the other Cloud ninjas, he'd start as an outsider but gradually earn their respect through his skills and determination. His relationship with his friends in Konoha might become more complex as he now has a new allegiance to the Hidden Cloud.
With Kakashi, it would be a complex situation. Kakashi might have tried to prevent Naruto's banishment but failed. When Naruto becomes Raikage, Kakashi would have to respect his new position. Naruto's relationship with the people of the Land of Lightning would start off as a bit of an outsider but as he becomes Raikage, they would look up to him. His relationship with the other Kage would also change. They would see him as a new player in the political and ninja world. Some might be skeptical of his sudden rise in the Land of Lightning, while others might be interested in forming alliances with him.
With his friends in Konoha, Naruto could be seen as both an asset and a potential danger. His friends might be in awe of his new abilities but also worried about how his connection to Cooler could draw unwanted attention to the village. His relationship with Kakashi could also change as Kakashi tries to help Naruto understand and control his new powers.
His relationship with Sasuke might become more complicated. Sasuke, who has his own dark past, might view Naruto's new identity with suspicion or envy. They could have more intense battles as Sasuke might see Naruto as a greater threat now.
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.
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.
With Kakashi, Kakashi would be extremely cautious around Naruto. He would be constantly on guard, worried that Naruto might inherit some of Fem Madara's more dangerous tendencies. Naruto would have to prove his loyalty and good intentions to Kakashi over time.
In this fanfiction, Naruto's abilities would change significantly. Firstly, he'd be exposed to Kumogakure's unique jutsu. He might learn more advanced lightning - style techniques which are prevalent in the Cloud Village. His combat style would be more brute - force - oriented, as the Raikage values strength. Also, his ability to lead and make strategic decisions would be molded by the Raikage's military - minded approach. He might not rely as much on his Uzumaki heritage in the beginning, but as he grows, he could find a way to combine the Raikage's teachings with his own innate abilities.
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.
With Kakashi, Naruto's relationship might shift. Kakashi would be intrigued by Naruto's newfound connection to Byakuya Kuchiki. He would have to adjust his training methods to incorporate Naruto's emerging Shinigami - like abilities. Naruto might also start to see Kakashi more as a guide in this new world of the unknown that his heritage has opened up.