One common plotline is Naruto leaving Konaha and finding a new place where he is truly accepted for who he is. He might meet new allies who help him grow stronger. Another is that he could be on a journey to prove his innocence, if the banishment was unjust. And sometimes, Naruto may discover a hidden power within himself during his exile.
Obviously, the new Hokage would be one of the main characters. It could be a character we already know like Naruto's son, who has inherited his father's determination and strength.
Definitely Iruka. He has seen Naruto grow up and has always supported him. Then there's Shikamaru. He's smart and he can see Naruto's value. He might support Naruto even if it goes against the village's decision at first. And of course, Kakashi. He has mentored Naruto and knows his potential, so he could be in Naruto's corner in these fanfictions.
Maybe the new Hokage is faced with a crisis within the village. For example, there is a rift between different ninja clans, and the Hokage has to use his/her diplomatic skills to bring peace. They could start by holding clan meetings and listening to each clan's concerns.
It could be a rogue ninja who was once a part of Konoha but was banished for unethical experiments. Now, with a thirst for revenge against Naruto and the village, he returns as a powerful and unpredictable foe.
One idea could be that Naruto, as the new Hokage, has to deal with a new and powerful enemy from a long - forgotten clan. This clan has a unique jutsu that can disrupt the chakra flow in the village. Naruto has to find a way to counter it while also maintaining peace within the village.
Perhaps a perk is the ability to shape the future of the ninja world. As Hokage, one can inspire the younger generation of ninjas. They can create new ninja academies or training programs. They also have the power to pardon or punish ninjas according to their deeds, which helps in maintaining law and order in the village.
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.
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.
Even Naruto himself could be a subject of this 'evil Hokage' concept in fanfiction. Maybe he is possessed by some dark entity or has a major change of heart due to some extreme event. This would completely change his character and turn him into an evil Hokage, which would be a very interesting and unexpected twist.