His relationship with his old friends would definitely change. He would have less time for casual training and hanging out. For example, his bond with Sasuke might become more formal as Naruto is now in a position of power. But they would still respect each other's roles.
With the other ninja villages, Naruto as the Fire Daimyo would need to maintain diplomatic relations. His relationships with the leaders of other villages would become more complex. He would have to balance the interests of the Fire Daimyo's territory with the overall stability of the ninja world. For instance, he might have to negotiate trade deals and security treaties more carefully.
His relationship with his old friends in the village would become more complex. They might see him as someone who has moved into a different social class. For example, Sasuke might view him with suspicion or envy, thinking Naruto has abandoned their shared past as shinobi.
With his new status and appearance, Naruto's relationship with his family would also change. His relationship with Hinata might face new challenges as he has to balance his duties as Daimyo with his family life. His children would grow up in a different environment, with Naruto being a figure of political power. And his relationship with the older generation, like Kakashi, would shift as they now have to respect him as a leader.
His relationship with Sasuke would be really interesting. Since Sasuke has his own complex connection to the Uchiha clan and Madara, Naruto becoming a Madara fan could either bring them closer together in understanding the Uchiha's past or drive them further apart if Sasuke doesn't agree with Naruto's new - found admiration. Maybe Naruto would start to push Sasuke towards a more 'Madara - like' view of power and revenge.
His relationship with Sakura would change a lot. Sakura might be initially scared of Naruto's fox form, but as she realizes it's still him inside, she would start to see him in a new light. She could become more protective of him. With Kakashi, Kakashi would be more cautious and observant, trying to figure out how to help Naruto control his new form. And with his rivals, they might either be more envious or more afraid of him now that he has this unique transformation.
His relationship with Sasuke would be very different. Sasuke might see Naruto as even more of an enigma. He could be both jealous of Naruto's new power and also concerned about what Naruto has become. Naruto, on the other hand, would try to show Sasuke that he's still the same person deep down.
Naruto's relationship with the villagers could be affected. As he becomes a Minato fan, he would try to uphold Minato's legacy even more. The villagers, seeing Naruto's newfound admiration for Minato, might start to see Naruto in a new light, more like how they saw Minato. Also, his relationship with Hinata could be different. Naruto might start to model his family - centered values after Minato, which could bring him and Hinata even closer as they plan their own family.
His relationships would change drastically. With his friends in the Hidden Leaf, there would be a sense of distance. For example, Sasuke might be confused by Naruto's decision. But at the same time, Naruto might form new relationships with the animals and plants in his hermitage area.
His relationship with Sasuke would become very strained. Sasuke, who has always been somewhat distrustful, would see Naruto as a real threat now. He might even consider Naruto an enemy and try to stop him.
Naruto's relationship with the other Leaf Village ninjas would also shift. Some might be suspicious of his new - found admiration for Itachi, especially those who were directly or indirectly affected by Itachi's actions. However, others who understand Itachi's true motives, like Kakashi, might support Naruto. This could create a complex web of relationships within the village, with Naruto at the center trying to balance his new beliefs and his old friendships.
His relationship with Sasuke would be severely strained. Sasuke, who has his own goals and views on power, would see Naruto's demon transformation as either a threat or a sign of weakness. He might distance himself from Naruto or even see him as an enemy to be defeated.