With his enemies, it would be a whole different story. Some enemies might be more hesitant to attack him knowing that he can't be killed easily. Others might be even more determined to find a way to kill him or use his immortality against him. Naruto would have to constantly be on guard against those who would seek to harm him because of his newfound state.
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 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 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.
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.
With Kakashi, Kakashi would be extremely worried. He would probably try to find a way to get Naruto out of Akatsuki without causing too much chaos. Naruto, on the other hand, would have to keep his distance from Kakashi to maintain his cover in Akatsuki, which would be a difficult situation for both of them.
Naruto's relationship with his sensei, like Kakashi, would change. Kakashi would be both proud and cautious. Proud because Naruto is getting stronger, but cautious as the Shinigami - related training is uncharted territory. His bond with the other villagers would also shift. Some might see him as a protector with new, otherworldly powers, while others might be suspicious of the Shinigami's influence on him. Overall, his relationships would be in a state of flux as he adapts to his new self after the training.