Perhaps in this fanfic, their personalities are made similar. Naruto is known for his determination, and Zetsu might be portrayed as having a similar unwavering focus towards a goal. Also, they could both be depicted as having a certain level of mystery about them. Naruto has the mystery of the Nine - Tails within him, and Zetsu has his own secrets in the original Naruto series, which could be enhanced and made more alike in the fanfic.
Well, one way could be in their physical abilities. Maybe in the fanfic, Naruto is shown to have some of Zetsu's stealthy movement skills, like being able to blend into the environment in a similar way. Another similarity could be in their connection to nature. Zetsu has a strong link to the plant - like aspects of nature, and Naruto's chakra might be shown to have a similar kind of connection in the fanfic.
In some fanfics, Naruto might have Zetsu's ability to blend into the environment or be as stealthy as him.
The fanfic might explore new aspects of Naruto's character by comparing him to Zetsu. It could show different sides of Naruto that we haven't seen before, like his more devious or strategic side if he takes on some of Zetsu's traits. This exploration of character depth can be really engaging for readers.
Zetsu's ability to split into two parts can be used to create interesting plot devices. For example, one part of Zetsu could be captured by the protagonists, while the other part goes on to execute a different part of the villain's plan.
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.
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.
I'm not sure specifically as there could be many different interpretations in fanfiction. But it might involve Zetsu using his unique abilities to rescue Naruto from a dangerous situation, like a powerful enemy attack or a life - threatening trap.
Perhaps Naruto controls Zetsu to help him in battles. Zetsu could act as a distraction while Naruto sets up his more powerful jutsu. For example, Zetsu could split into multiple forms and confuse the opponents, giving Naruto an opening to attack.
Zetsu could be a mysterious informant in a Naruto fanfic. He could be lurking in the shadows, gathering information for either the good guys or the bad guys and providing crucial intelligence that changes the course of events in the story.
Sasuke would be a likely character to interact. Given their complex relationship throughout the Naruto series, Sasuke might be suspicious or intrigued by Naruto's control over Zetsu. Their interactions could range from confrontations to reluctant teamwork.
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.