Obito's influence would likely make Naruto more aware of the darker side of the ninja world. Naruto is usually very optimistic, but with Obito's guidance, he would see the hardships and betrayals that can happen. For example, Naruto might become more cautious in his trust of others.
His personality would change in several ways. For one, he'd have to be more cautious. Obito was involved in a lot of secretive and dangerous operations. Naruto would have to adapt to this new level of secrecy. Also, he might become more brooding as he tries to understand Obito's darker motives in the original story. But ultimately, his strong belief in friendship and his never - give - up attitude would still be there, and he'd use them to make different choices than Obito did.
Naruto's usually sunny and optimistic personality might become a bit more brooding. Since he's in Obito's body, he might be influenced by the memories of Obito's tragic past. However, he would still try to hold on to his core values of friendship and never giving up.
It could change it a great deal. For one, Obito might not be as much of a villain. His alliance with Naruto could lead to a united front against Madara much earlier. This would mean less destruction and death in the ninja world. Also, Naruto would have a powerful ally who has a deep understanding of the Sharingan and its powers. They could develop new jutsu together, changing the power dynamics in battles.
Naruto might become more reserved. Since Obito has a more brooding personality, Naruto could pick up on some of that. His once - bright and exuberant nature might be tempered.
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.
Harry would likely become more cynical. Obito's experiences of betrayal and loss could make Harry less trusting. He might also become more secretive as he tries to figure out these new memories on his own.
Naruto's fighting style would likely become more stealth - oriented. Since Obito is known for his ability to move undetected, he might teach Naruto some techniques to blend into the shadows and surprise his opponents. For example, Naruto could learn to use the environment to his advantage in a more subtle way, rather than his usual straightforward attacks.
Naruto's fighting style would change significantly. He would no longer rely solely on his brute strength and Rasengan - based attacks. The Sharingan would allow him to see the flow of chakra more clearly, so he could target his opponents' weak points more precisely. He could also use genjutsu, which he has little experience with before. Maybe he would combine his shadow clones with the Sharingan's abilities, for example, having clones with Sharingan - enhanced vision to scout the area better during a battle.
If Naruto has Obito's eyes in fanfiction, his abilities would be enhanced in several ways. The Sharingan's ability to see chakra flow clearly would allow Naruto to better analyze his opponents' moves and weaknesses. With Kamui, he could teleport himself or objects, which would be a huge advantage in battles. He might also be able to use some of the more advanced Sharingan - related genjutsu, adding another layer to his combat skills.