In this fanfic, Naruto might have chosen to be a sort of wandering protector. He moves from village to village, helping those in need, fighting against common threats like the Akatsuki but not being tied to one village as Hokage. He could be a symbol of hope across all ninja lands, rather than just for Konoha.
One possibility could be that Naruto focuses more on his training to become a super powerful ninja without the burden of being Hokage. He could travel the world, learn new jutsus from different regions, and form alliances with various ninja clans on a more personal level rather than as a Hokage.
One possible storyline could be that Naruto decides to focus on traveling the world instead of becoming Hokage. He could use his skills to help people on a more individual basis across different villages. He might learn new jutsu from various shinobi cultures and become a sort of wandering hero.
Perhaps he would focus on his training and become a master of a new, unique form of jutsu. He might then open a dojo to teach the younger generation his skills, rather than aiming for the Hokage position. This way, he could still have a great influence on the ninja world.
Shikamaru is another possibility. He is known for his strategic mind. As Hokage, he could use his intelligence to make wise decisions for the village. He may not have the brute strength of Naruto or Sasuke, but his ability to plan and analyze situations would be invaluable in leading Konoha.
Sasuke could be an alternative. He has strong ninja skills and a deep understanding of the ninja world. His experiences have made him grow into a very capable person, and his Sharingan gives him an edge in combat and strategic planning.
Naruto's strong sense of individual freedom might also be a hindrance. He has always been a bit of a maverick, doing things his own way. As Hokage, he has to follow certain protocols and rules, and his independent streak could clash with the more structured and traditional role of Hokage.
One possible path is that Naruto becomes a traveling ninja, similar to Jiraiya. He could go around different villages and countries, learning new jutsus and making friends without the burden of leading a village. He might focus on spreading the message of peace in a more direct, personal way.
Sasuke could also be a possibility for the 6th Hokage in the fanfic. He has grown stronger over the years and his unique perspective on the ninja world could bring new ideas to the leadership of the Hidden Leaf. He might start off as a controversial choice but prove himself through his actions in protecting the village and making tough decisions.
One possible plot could be Naruto having to prove himself to the village elders. He might start by implementing new training programs for the younger ninjas, inspired by his own journey. He could also focus on improving relations with other villages, using his charisma and unique perspective as someone who was once an outcast.
Perhaps the Hokage has made a decision that Naruto believes will destroy the village's future. Like if the Hokage decides to sacrifice a large number of innocent villagers in order to achieve a short - term goal. Naruto, with his strong sense of justice, might see killing the Hokage as the only way to stop this madness.
One possible plot could be Naruto dealing with the boredom of retirement. He might try to find new hobbies like gardening in Konoha. Maybe he starts teaching some young ninja in an unofficial way, passing on his unique skills and experiences.