One common way is that Naruto becomes more romantic. He might start writing poems or giving Sakura flowers, which is a far cry from his usually rough - and - tumble self. This is his way of showing his love for her in the fanfiction world.
In some fanfictions, Naruto might join Anbu because of Sakura to prove himself worthy of her. Maybe he thinks that by becoming an elite Anbu member, he can show her that he's strong and reliable.
In fanfiction, Naruto's character can change in terms of his social skills. Since he has a strong affection for Sakura, he may become more outgoing and sociable in an attempt to get closer to her. He could start spending more time with Sakura's friends, which is a big change from his previous focus mainly on his own small group of friends. His values might also shift. For example, he might start to value Sakura's opinions more than anyone else's, and this could influence his decisions in various aspects of his life, like when choosing missions or dealing with village politics.
In the official Naruto canon, there is no such event where Naruto is banished because of Sakura fanfiction. The Naruto storyline follows a set plot created by the original author, and this kind of out - of - the - blue scenario doesn't exist in the real Naruto world.
One possible change is that she becomes more self - reliant. In the Wave arc, she saw the limitations of her own abilities. So in fanfictions, she might start to focus on self - improvement. Maybe she begins to practice her combat skills more rigorously, so that she can hold her own in battles without always depending on Sasuke or Naruto.
In this type of fanfiction, a major theme is often the fragility of the male ego in the face of unrequited love. Naruto, despite his strong exterior, is broken by Sakura's lack of romantic interest. Another theme could be the idea of lost hope. Naruto may have hoped for so long that Sakura would come to love him, but when that hope is finally extinguished, he sees no reason to continue living. Additionally, themes of loneliness and isolation might be present as Naruto may feel completely alone in his unrequited love for Sakura.
Well, if this were to happen in some alternate, non - canon story, the entire dynamic of the Naruto universe would shift. Naruto's friends would be divided. Some might support him and think the banishment was unjust, while others might believe in the reasons given in the fanfiction. Sasuke's story would also be affected as Naruto's banishment could change Sasuke's view of the village even more. And the Akatsuki would have an easier time causing chaos without Naruto there to oppose them.
Often, the theme of self - discovery is present. By changing the past, Sakura gets to learn more about herself and her capabilities. Also, the theme of preventing a tragedy is quite common. Maybe there was a big disaster in the original timeline that she aims to avoid. In these fanfictions, the exploration of the butterfly effect is also a thing. Every change she makes in the past has consequences in the future, and this can lead to interesting plot developments.
Perhaps he would change to Naruto Storm. 'Storm' can represent his powerful and sometimes tempestuous nature. In the series, Naruto has shown great strength and determination that could be likened to a storm, which is both destructive and at the same time a force of change.
I'm not sure of specific 'sakura changes the past fanfiction' titles off - hand. You could try searching on fanfiction websites like Archive of Our Own or FanFiction.net. They usually have a large collection of fanfictions on various topics.