The story would likely diverge from the original plot a great deal. Since Naruto is a prototype, there could be a new group of antagonists who are interested in his unique nature. His training would also be different, perhaps involving more scientific or experimental methods. His bond with his mentors like Jiraiya might be affected as they try to understand and guide this new 'prototype' Naruto. Also, the political situation in the ninja villages could change as other villages might see him as a threat or an opportunity due to his prototype status.
Well, his journey would be completely different. Instead of following the traditional ninja path, he'd be on a journey to understand and master his new naga abilities. His goals might shift from protecting the village in the normal way to perhaps protecting a new community of naga or finding a way to co - exist between humans and nagas.
If Naruto becomes cold - hearted, his relationships with the villagers would change drastically. The villagers, who once saw him as a hero, would now be faced with a cold and unapproachable Naruto. Children who used to look up to him would be scared. His friends from the Akatsuki days, like Nagato, might even see this new Naruto as a threat. Overall, his relationships would go from being warm and friendly to cold and distant, filled with suspicion and unease.
He'd become more responsible for the whole world perhaps. Since the Avatar has to keep balance everywhere.
If Naruto becomes a nukenin, his relationship with the village elders would be completely severed. They would see him as a threat, and he would see them as unjust. With his peers, some might side with him, believing in his innocence. Others would follow the village's orders out of loyalty. His bond with the Nine - Tails would also change. The Nine - Tails might offer more support, seeing Naruto as an outcast like itself.
His relationship with Sasuke would be greatly affected. Sasuke, who has his own experiences with the idea of killing, might see Naruto in a new light. They could either become rivals again or Sasuke might try to 'save' Naruto from his new dark path. With Sakura, she would be horrified. She's always seen Naruto as a positive force, and this change would make her question everything. She might even try to use her medical skills to 'cure' Naruto of his new - found killer tendencies.
If Naruto becomes a Saiyan in fanfiction, his relationship with his mentor, like Jiraiya, could be different. Jiraiya would have to guide Naruto in handling these new Saiyan powers. Naruto's friends might be both in awe and a little scared. For example, Sakura might be worried about Naruto losing control of his new powers. And his relationship with the villagers could change too. Some might see him as an even greater protector, while others might fear his new, more alien - like powers.
His abilities would become more lethal. Instead of using his Rasengan to just defeat opponents, he might use it to kill. His speed and stealth would be enhanced for more effective assassinations. His ability to gather information, like he did as a ninja, would be used in a more sinister way to track down his targets.
If Naruto becomes a Jigsaw fan in fanfiction, his relationships would change drastically. His friends and comrades in Konoha would be confused and concerned. They have always known Naruto as a kind - hearted and positive person. His newfound interest in Jigsaw's ways would seem out of character. For instance, his bond with Hinata would be severely tested. Hinata, who loves Naruto for his heroic and gentle nature, would be at a loss on how to deal with this new, darker Naruto. His relationships with the other ninja clans in the village would also become tense as they would view his new ideology as a threat to the village's peace and stability.
Well, when Naruto becomes the Death God in fanfiction, his relationship with Sakura would change. She might be more hesitant around him, as his new power is so otherworldly. And his bond with Kakashi would also be different. Kakashi, being a wise ninja, would try to guide Naruto in using this power responsibly. Naruto's relationships with the villagers would shift too. Some might worship him, while others could be suspicious of his new - found power.
Well, his relationship with the village as a whole would be one of enmity. But on an individual level, some of his friends might secretly support him. Naruto would likely be more cautious about trusting new people. His connection with the other jinchuriki might become stronger as they can relate to his situation of being an outcast. His relationship with Kakashi - sensei would be filled with conflict. Kakashi would have to balance his duty to the village and his feelings for Naruto, who he has trained and cared about.