Naruto's relationship with the Hidden Leaf Village as a whole could change. The village elders might view him differently, either as a potential threat if they don't understand the power of the transplanted eye, or as a new hope for the village if they see the potential in his new ability. This could lead to Naruto having to prove himself all over again to gain the trust of the village.
His relationship with Sasuke might become more complicated. Since Sasuke is an Uchiha and Naruto now has an Uchiha - like power through the transplanted eye, Sasuke could be jealous or feel that Naruto is encroaching on his family's legacy. On the other hand, it could also bring them closer as they now share a similar power source.
His relationship with the Leaf Village would become more personal. He'd be part of the Sarutobi clan in a sense. His bond with Shikamaru and Choji would strengthen as they are Asuma's students. Naruto would also have a new father - figure relationship, which would change how he views authority.
His relationships could change quite a bit. His friends might be a bit intimidated at first. For example, Sakura might be worried about this new, unknown power. But over time, they would probably come to accept it. His enemies, on the other hand, would be more cautious around him.
His relationships with his friends would likely be strained at first. They might be jealous of his immortality or worried about how it will change him. For example, Sasuke might see Naruto's immortality as another way that Naruto is 'better' than him, which could lead to more conflict between them. However, over time, his true friends would come to accept it and see it as a way to keep Naruto around forever.
His relationship with Sasuke might change. Sasuke might initially be confused or even critical of Naruto without his headband. But as Naruto shows his determination without it, Sasuke could gain a new respect for him. With his friends like Sakura, they might be more protective of Naruto, fearing that others will target him without the symbol of his ninja status.
His relationship with Sasuke would be very different. If Naruto stops the Uchiha massacre, Sasuke may not have the intense hatred he had in the original story. They could grow up as friends without the need for Naruto to constantly chase after Sasuke to bring him back.
In this fanfic, Naruto's relationships would be in flux. Regarding his friends, they would look up to him as he gains knowledge and power from the Sannin. His relationship with Sakura could change as he becomes more capable of handling Sasuke - related issues. With the village elders, Naruto might gain more respect as they see his potential growing under the Sannin's tutelage. His connection with the Nine - Tails would also be different. As he learns from the Sannin, he could use the Nine - Tails' power in new ways, which might change how he is perceived by the fox and how he interacts with it. All in all, his relationships would be reshaped by the new experiences and skills he acquires from the three Sannin.
With Sasuke, things could get more complicated. Sasuke might see Naruto's new bloodline as another way Naruto is getting stronger while he struggles to reach his own goals. This could fuel their rivalry even more, or it could lead Sasuke to try and understand Naruto's new situation in an attempt to gain an edge himself.
His relationship with Sasuke would be greatly affected. Sasuke might see Naruto as more of an equal in terms of their eye powers. They could have a new level of understanding or even rivalry. It might also make Sasuke more protective of Naruto in a strange way, since the Sharingan is precious to the Uchiha.
In terms of his romantic relationships, if there was a budding relationship with Hinata, for instance, his new status as a jounin could either strengthen their bond as she admires his achievement, or it could create some distance as he has more duties and less time for personal matters.
Naruto's friends might be initially suspicious of the new skills and attitude he gets from Slade's training. For example, Sasuke could see Naruto's new combat style as too ruthless and this could create tension between them. Sakura might worry that Naruto is getting too influenced by a dangerous figure. However, if Naruto can show that he's still the same person at heart, they could gradually accept his new abilities.