Perhaps Itachi realizes that Naruto has the potential to change things for the better in the ninja world. He takes Naruto with him to train him in ways that the Leaf Village couldn't. Itachi may have some knowledge or skills that he wants to pass on to Naruto, like how to deal with the power of the Nine - Tails in a more efficient way.
In the fanfiction, Itachi could take Naruto with him because he sees a kindred spirit in Naruto. Naruto's determination to protect his friends and the village reminds Itachi of his own values. He wants to guide Naruto on a path that will prevent Naruto from making the same mistakes he did. Also, Itachi may believe that together, they can uncover some secrets that are important for the well - being of the entire ninja community.
Itachi could take Naruto from the academy to keep him safe. There might be some hidden enemies in the academy who are targeting Naruto.
Well, in some fanfictions, Naruto might use his shadow clones to search every possible location. Once he locates Sasuke, he could use his strong bond and persuasion skills to convince Sasuke to come with him. Naruto might remind Sasuke of their past friendship and the dreams they once shared, like protecting the village together.
He could be touched. Despite his stoic exterior, Itachi may see this as a genuine and innocent gesture from Naruto, and it could warm his heart in some way. Maybe he starts to see Naruto in a new light, as someone who can bring a bit of light - heartedness into his world of shadows.
Naruto would adapt to Itachi's life in several ways. Socially, he'd have to get used to Itachi's connections and rivalries. For instance, his relationship with Kisame would be different as Naruto. He might try to influence Kisame in a more positive way. Emotionally, he'd have to deal with Itachi's internal struggles. Itachi had a lot of guilt and secrets, and Naruto would have to either come to terms with them or find a way to resolve them. And in terms of combat, he'd practice Itachi's signature moves over and over to make sure he could use them effectively in battle.
Well, it's popular because Itachi and Naruto are both very popular characters in the Naruto series. Fans like to see the dynamic between them. Itachi is this mysterious and powerful ninja, and Naruto is the energetic and determined hero. When Itachi protects Naruto, it creates an interesting contrast and a new aspect to their relationship that wasn't fully explored in the original series.
Naruto might initially be shocked and angry. He has a strong sense of justice and being kidnapped goes against everything he stands for. He would likely try to fight back immediately, using his basic ninja skills and his determination. For example, he could try to use his Shadow Clone Jutsu to create distractions and escape.
At first, it's likely to be very awkward. Naruto is a very open and energetic person, while Itachi is more reserved. But as they are forced to spend time together because of the arranged marriage, they start to find common ground. For instance, they both care deeply about protecting the village in their own ways.
They might go on a journey to discover the secrets of Itachi's past. Naruto could learn a lot from Itachi about the Uchiha clan and their powers. Maybe they'll encounter other powerful ninja clans along the way and have to fight or make alliances.
In some fanfictions, it could be through a special jutsu or ritual. Maybe Itachi, before his death, transferred his Sharingan to Naruto in a unique way, perhaps using a forbidden technique that was known only to a few in the Uchiha clan.
Naruto may become more calm and composed. Itachi's presence and training methods would likely instill a sense of discipline in Naruto. He'd probably be less impulsive in battles and think more before acting.