His relationship with Sasuke might be affected. Naruto might approach Sasuke differently, with new strategies learned from Zetsu. He could be more secretive about his intentions towards Sasuke, which might either make Sasuke more curious or more distrustful. With his friends in Konoha, they might be a bit wary of Naruto at first because of his new training source. But once they see that Naruto is still on their side, they would support him.
If Naruto was trained by Zetsu in a fanfic, his relationship with Kakashi would likely change. Kakashi might be concerned about the influence Zetsu has on Naruto. He could try to counteract some of the teachings he thinks are too dangerous or unethical. Naruto, on the other hand, might see Kakashi's concerns as over - protection and start to distance himself a bit. His bond with Sakura could also be different. Sakura might be scared for Naruto, thinking that Zetsu is corrupting him, and Naruto would have to prove to her that he's still the same Naruto deep down.
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.
He may develop a more calculating side. Black Zetsu is all about manipulation. Naruto could start thinking several steps ahead in a more devious way. For example, he might start using people's weaknesses against them, which is completely against his original nature. This change in personality would likely cause a rift between him and his friends who know him as the always - honest and straightforward Naruto.
If Naruto was trained by the Akatsuki in fanfiction, his relationships would be completely transformed. For starters, his relationship with Kakashi would be strained. Kakashi has always been Naruto's mentor in a way, and seeing Naruto side with the Akatsuki would be a shock. His friends like Sakura and Shikamaru would also be confused and probably try to bring him back to the 'right side'. And his relationship with the villagers of Konoha would turn sour as they would fear his new - found Akatsuki - related powers.
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.
In a fanfic where Naruto is trained by Zetsu, the story could take an interesting turn. Zetsu has knowledge of the Akatsuki and their secrets. Naruto could learn about the organization from the inside out. This knowledge could help him in his quest to bring peace. He might also gain some physical enhancements. Zetsu is quite durable in his own way, and Naruto could inherit some of that sturdiness. This would make him an even more formidable opponent in battles against strong foes like Pain or Madara.
With Sakura, Naruto's attitude could shift. Instead of being the goofy, love - stricken Naruto she's used to, he could become more distant. He might be so focused on his training with Zabuza that he doesn't have time for Sakura's attempts to get his attention. This could make Sakura feel rejected and lead to some tension between them.
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.
His combat abilities would become more diverse. Madara could teach him new forms of taijutsu and ninjutsu. For example, Naruto might learn some of Madara's signature space - time ninjutsu, which would give him an edge in battles. His chakra control would also improve as Madara is very proficient in chakra manipulation.
He might become more cautious. Tsunade is a more calculating ninja compared to some of Naruto's previous mentors. So Naruto could start to think before he leaps, rather than just charging into battle head - first all the time.
His relationship with his friends would likely change. He might become more distant at first as he focuses on his training with the female shinigami. But in the long run, his new powers and insights could make him a better protector of his friends. For example, he could use his newfound skills to rescue them from more dangerous situations.