Sure does! Naruto becomes Hokage after going through numerous battles and proving his worth. It's a well-earned title that showcases his dedication and the respect he gains from his peers and the village.
In some fanfictions, Sakura might become Hokage through her exceptional medical skills. She could save the life of an important figure during a major crisis, and as a result, gain the respect and support of the village to take on the role. For example, if she cured a widespread disease that was plaguing the Hidden Leaf.
There are various types. Some might focus on Naruto's intense training and growth to earn the title. Others could involve unexpected challenges and how he overcomes them to become the Fifth Hokage.
One common theme is redemption. Since Kakashi can go back in time, he often tries to make up for past mistakes or prevent tragedies that occurred in the original timeline. For example, he might try to save a character who died before. Another theme is the changing of fates. He can change the destiny of not only himself but also of his friends and the whole village. He can use his knowledge of future events to better prepare for threats.
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.
One possibility is that there would be a lot of reminiscing. Team Minato was Kakashi's old team. They might talk about old missions, like the one where they faced the Stone ninjas. Kakashi could share how their teachings influenced his leadership as Hokage.
His godlike power could also change the way he approaches the role of Hokage. Instead of relying on traditional ninja skills and strategies all the time, he might introduce new ways of governing the village based on his unique powers. He could use his power to create new defenses or improve the living standards in the village more rapidly.