His relationship with Sasuke would likely become more of a partnership. As Hokage, Naruto would need Sasuke's skills and knowledge to protect the village. They would probably have regular meetings to discuss security and other important matters.
With Sakura, Naruto would now be in a position of authority. Their friendship might still be there, but there could be a new level of respect from Sakura towards Naruto as the leader of the village. And Naruto might rely on Sakura's medical skills more often for the well - being of the village ninjas.
His relationship with his parents would be very strange. If he goes back to a time when his parents were alive, he would have to hide his true identity. But he could also get to know them in a way he never did. He might be able to change their fates as well, which would have a huge impact on his own life and the entire Hidden Leaf Village.
His relationship with his teachers would also change. For example, with Iruka - sensei, Naruto could show his gratitude in a more profound way. He could also use his skills as the Seventh Hokage to help Iruka in ways he couldn't before. And with Kakashi - sensei, Naruto could offer insights into future threats and how to better train the next generation, strengthening their bond as teacher and student even more.
It could strengthen Naruto's relationship with Iruka. Since Naruto is the son of the fourth hokage, Iruka might see Naruto as an even more important part of the village and be even more protective. For example, he could be more involved in Naruto's advanced training.
His relationship with Sasuke would likely be affected. Sasuke might see Naruto being forced into this role and feel that Naruto is losing his freedom, which could either make Sasuke more protective or more distant. Naruto's friendships with the others like Shikamaru would also change. Shikamaru, who has a good understanding of leadership, might become more of a mentor - like figure to Naruto in handling the political aspects of being Hokage.
If Naruto doesn't become Hokage, his relationship with Sasuke might be less strained. Since there's no need to compete for the top position in the village, they could focus more on their friendship. They might go on missions together more often just for the sake of adventure and to protect each other.
If Naruto travels back to the past, his relationship with his parents would be completely different. He would finally get to meet them as an adult and be able to have proper conversations with them. He could share his experiences and they could give him advice from their own wisdom.
His relationship with Sasuke would likely become more of a partnership. They would work together to protect the village and the ninja world. With Sakura, Naruto might become more of a respected leader figure, and she could be one of his most trusted medical ninjas. And for Kakashi, Naruto would now be his equal in terms of leadership, and they would probably exchange ideas on how to better lead the village.
Her relationship with Sasuke would be very different. If she time - travels back, she might be able to approach Sasuke in a more mature way as a Hokage. Instead of just chasing after him out of friendship and rivalry, she could offer him real solutions to his problems and help him find his place in the village without leaving.
He would become more responsible. As Hokage, he has to think about the whole village, not just his friends. So he might be a bit more serious, but still keep his positive and energetic side.
Under Naruto as the 5th Hokage in fanfiction, the village would experience a cultural shift. Since Naruto values all kinds of people, the village would be more open to different ideas and ways of life. New forms of ninja techniques might be developed as he encourages everyone to explore their potential. Also, the village's defenses would be strengthened not just by physical means but also by the strong bonds between the villagers, which Naruto would foster.