Naruto might give Itachi some traditional Konoha food as a gift. Since Itachi has been away from the village for a long time, he might miss the taste of home.
One popular fanfiction might involve Itachi passing on a unique jutsu to Naruto. For example, a Sharingan - related power that Naruto can use in a creative way against tough enemies. This could change the dynamics of his battles and how he is perceived in the ninja world.
I'm not sure about a specific one off - hand, but you can check out fanfiction websites like Fanfiction.net or Archive of Our Own. Just search for 'Itachi gives Naruto power' and you'll likely find a bunch of different stories. Some might focus more on the action aspect, while others might explore the emotional side of Itachi's decision to give Naruto power.
One possible plot twist could be that Naruto struggles to control Itachi's power at first. Since Itachi's power is very different from his own chakra nature. For example, Itachi's genjutsu abilities might be too much for Naruto to handle initially, leading to him accidentally using it on his friends, causing mistrust among them. Another plot twist could be that the Akatsuki targets Naruto more aggressively, believing he has become a greater threat with Itachi's power. They might send their most powerful members after him, like Pain or Obito. Also, Naruto might discover some hidden secrets about Itachi's power that even Itachi was unaware of, which could change the course of the shinobi world's power balance.
Itachi could have realized Naruto's potential and determination. He knows Naruto is different from other ninjas and has a unique ability to change people's hearts. By giving Naruto his Sharingan, Itachi might be ensuring that Naruto has the power to carry out some important mission or to protect the people Itachi cares about.
One reason could be for strategic purposes. Itachi was a highly strategic ninja. So, in fanfiction, Naruto might act like him to outwit a particularly difficult enemy. For instance, when facing an enemy who is a master of deception, Naruto could adopt Itachi's calm and calculating demeanor to see through the enemy's tricks.
His relationship with Sasuke would become extremely complex. Sasuke might see Naruto as a reminder of Itachi, which could stir up a mix of emotions like anger, envy, and also a strange sense of kinship. Naruto, on the other hand, might try to use Itachi's power to understand Sasuke better, but this could be misinterpreted by Sasuke as Naruto trying to take on the role of Itachi in his life. With his friends like Sakura and Kakashi, they might be initially wary of Naruto's new power. Sakura might worry that Naruto is losing himself to Itachi's power, while Kakashi would be more cautious and observant, trying to guide Naruto to use the power in a positive way.
They could develop a mentor - mentee relationship. Itachi, with his vast knowledge and skills, could guide Naruto. Naruto, in turn, could show Itachi his unwavering spirit, which might even inspire Itachi in some ways.