Maybe Naruto admires Kakashi's skills. Kakashi is a highly respected ninja, and Naruto might want to be as good as him. So he starts acting like him to learn from him.
Well, Naruto could mimic Kakashi's calm and collected demeanor during fights. Kakashi is known for not getting flustered easily. Naruto might start to hold back his usual exuberance and be more stealthy, like Kakashi sneaking up on enemies. He could also try to use a variety of jutsu in quick succession, similar to how Kakashi combines different techniques smoothly in battle.
In a 'naruto acts like gin fanfiction', Naruto might be quieter and more observant. Instead of his usual boisterous self, he could be more like Gin, who is often sly and calculating. Maybe he would have a more subdued way of showing his power and a different approach to his enemies.
One possible plot could be that Naruto, after being exposed to some strange chakra or magic, starts to take on Grimmjow's aggressive and fearless attitude. He might become more impulsive in battle, like Grimmjow, and start to challenge his enemies without much thought for strategy at first. His friends would be confused by this sudden change in his behavior.
Well, one possible plot could be that Naruto starts to adopt Pain's view on justice. He might see the world as a place full of suffering that needs a radical change. He could begin to question the traditional ways of the Hidden Leaf Village and try to implement some of Pain's ideas in a more positive way, like finding a new system to ensure peace that doesn't rely solely on the power of the ninja villages.
If Naruto were to act like Yujiro in a fanfiction, it would change his relationships too. He would no longer be the overly - friendly Naruto we know. He might become more aloof and selective with his friendships. His interactions with Sasuke could be different. Instead of constantly trying to bring Sasuke back with kindness, he might use a more forceful and intimidating approach, just like Yujiro would deal with those who oppose him.
Maybe there's a plot where Naruto is influenced by an external force that makes him act like the Joker. He then starts to target the powerful figures in the ninja world, not to defeat them in a traditional sense, but to expose their weaknesses and make them look foolish, just like the Joker does with Batman. And as he does this, his relationships with everyone around him start to crumble.
Sakura would be worried sick. She'd try to figure out what happened to Naruto to make him act this way. She might try to talk to him, use her medical ninjutsu to check if he's under some kind of genjutsu or has some other problem. She'd be very vocal about her concerns and would try to get the other villagers to help bring Naruto back to his normal self.
Maybe Naruto is put in a situation where he feels that Hiruzen's way of handling things is the best option. For instance, if there is a major crisis in the village that requires a more traditional and experienced approach, Naruto might choose to act like Hiruzen. Also, he could be influenced by the stories he has heard about Hiruzen and wants to fill his shoes in a way.
His friends would be the most affected. People like Sakura and Kakashi who know Naruto well. Sakura is used to Naruto's kind - hearted and determined self. If he starts acting like Grimmjow, she'd be very confused and worried.