How would Naruto's relationships change if he was raised by the Inuzuka in fanfiction?

His sense of smell would likely improve significantly. Since the Inuzuka clan has a strong connection with their ninja dogs and are known for their enhanced sense of smell, Naruto would be trained in this area. This could help him in tracking enemies or finding hidden objects much more easily than in the original story.

His relationships would be very different. He wouldn't have the same connection with Jiraiya, for example. Instead, he might be mentored by an Iwagakure ninja. His relationship with the other villages would be more strained, as Iwagakure has a different history of relations with them. And his relationships with his peers in Iwagakure would be based on the Iwagakure way of life.

If Naruto was raised by Orochimaru in fanfiction, his relationships would be turned upside down. His friendships from the Leaf Village would be in jeopardy. Since Orochimaru is not one to value the kind of loyalty and friendship that Naruto's friends in the Leaf do, Naruto would have a hard time understanding and maintaining those relationships. He might even be hostile towards them, seeing them as obstacles in his pursuit of power. His relationship with the Hokage would also be a mess. Instead of looking up to the Hokage as a role model, he would probably view the position as something to be conquered or undermined, following Orochimaru's ideology of power - seeking.

If Naruto was raised by Obito, his relationships would take a radical turn. With the villagers, he would be seen as an outsider or even a threat, just like Obito was in a way. His relationship with Sakura would be different too. Without the common experiences in the village, he might not have the same friendly - rival kind of relationship with her. And his relationship with the Akatsuki members could be very different. He might be more inclined to understand their motives or even join them at some point, given Obito's connection to the group. It would create a whole new web of relationships that are far removed from what we saw in the original Naruto story.

Naruto's relationships would experience a significant shift. With Sarutobi as his guardian, he would have a closer relationship with the Anbu. He would be more involved in the inner workings of the village at an earlier stage. His relationship with Kakashi would also be different. Instead of Kakashi being his main mentor, Sarutobi would play that role. This would mean that Naruto would approach his training and missions with a different mindset, which in turn would affect how he relates to his comrades and opponents.

Naruto's relationships would be transformed if raised by Gogeta in this fanfiction. His connection to his village would be different. He might not feel as strong of an emotional attachment to Konoha as he did in the original story. In terms of his friends, he would be more of a loner in a sense, but also a figure of mystery and power. His relationship with Kakashi would also be altered. Instead of Kakashi being his main teacher, Gogeta would fill that role. This could lead to Naruto having less of a traditional ninja - like view of relationships and more of a Saiyan - influenced view, which could be more about strength - based alliances and mutual respect for power.

His relationship with Sasuke would be different. Instead of the rivalry born out of their time in Konoha, it could be more of a friendly competition between two powerful clans. Naruto, being Uzumaki - raised, would have a different perspective on power and friendship.

Naruto's relationship with his friends in the Leaf Village would be altered significantly. He would have a more distant relationship with them. Since he was raised in Mt. Myoboku, he would have closer bonds with the toads instead. His idea of friendship might be more in line with how the toads interact with each other, which could make it hard for him to fully connect with his human friends at first.

His relationship with the Hidden Leaf would be strained. He might see the village as a source of weakness rather than a place to protect. And his friends in the village, like Sasuke and Sakura, would be more like strangers to him. He would not have the same bonds that were formed through growing up in the Leaf.

His relationship with Sasuke could be different. Maybe Sasuke would be in awe of Naruto's new powers at first. They might have less of a rivalry and more of a partnership from the start, with Sasuke seeing Naruto as a step ahead in power and knowledge.