Well, in the 'Naruto relives his life fanfiction', Naruto could potentially change the relationships in the Hidden Leaf Village. He might be able to reach out to characters like Sasuke in a different way, since he already knows Sasuke's pain and struggles from his first life. This could lead to a more harmonious bond between them much earlier in the story.
Sasuke is definitely one. Since Naruto already knows Sasuke's path in his previous life, he could change Sasuke's fate. Also, Kakashi. Naruto might interact with Kakashi differently, sharing his future knowledge which could impact Kakashi's decisions.
If Percy relives his life, he could completely rewrite the prophecy. He may not make the same mistakes that led him to fulfill the prophecy in the original way. Instead, he could find new ways to deal with the threats to the demigod world, like finding alternative solutions to the problems caused by the Titans and the Giants. He could also have a chance to explore more about his mother's side of the family, which was not much delved into in the original story.
One possibility is that Percy relives his life and focuses on training more intensively. He could learn new skills or magic earlier, which would change the course of his adventures. Maybe he would be more strategic in battles, and as a result, save more people and gain more respect in the demigod community.
He'd likely become more confident. Since he already knows what he's capable of, he can show it right away. For instance, in his first encounter with a monster, he won't be as scared and will be more assertive in using his powers.
It could be that a new character, someone from a far - off land that Naruto met during one of his travels, is involved in his secret life. This character could bring with them a different culture and set of skills that Naruto is learning from in secret, perhaps something that could revolutionize the way ninjas in the Hidden Leaf operate.
Obviously, Naruto will be the main character as the story is about him restarting his life. Sasuke is also likely to be a main character as he was Naruto's rival and friend in the original series. Kakashi too, as he was Naruto's teacher and mentor, will probably play an important role in this new story as well.
An interesting aspect could be the family traditions. Naruto would learn about his family's history and traditions from his parents. For example, there could be a special family celebration that Naruto gets to experience. His parents could also introduce him to other powerful ninja families, which could lead to new friendships and alliances for Naruto. This would not only enrich Naruto's personal life but also his standing in the ninja community.
One interesting plot point could be Naruto having the knowledge from his previous life and using it to train more effectively from the start. For example, he might focus on different jutsu or skills that he overlooked before. Another could be his changed relationships. Maybe he decides to befriend some characters earlier or handle his relationship with Sasuke in a more proactive way in this new life.