Madara Uchiha could also be the main character in this type of fanfiction. Although in the original story his actions are mostly related to his grand plans for the Ninja world, in a fanfiction, it could be explored what would happen if he decided to leave Konoha specifically because of his Rinnegan and the power it holds.
One possible reason could be a search for power. The character might feel that Konoha doesn't offer enough resources or training opportunities for them to fully explore the potential of the Rinnegan. They may believe that there are other places in the Naruto world where they can gain more knowledge and power related to their special eye.
It could be Sasuke. If he were to turn to the dark side in the fanfiction, his Rinnegan powers could be used to destroy Konoha. He has the potential to be extremely powerful and if he has some sort of vendetta or is influenced by some dark force, he might take his anger out on the village.
Another scenario is that Naruto leaves because he feels like an outcast with the Rinnegan. The villagers might fear his new power, and he decides to leave to find a place where he can fully understand and control the Rinnegan without causing panic. He could then encounter other powerful ninjas or groups who either want to use him for his power or help him master it.
The main antagonist could be a new character. For example, a powerful ninja from a rival village who has a vendetta against Konoha. This ninja could manipulate Naruto into leaving Konoha by spreading false rumors about the village. Then, he tries to use Naruto's power as an assassin for his own evil plans.
Maybe the main antagonist is a powerful figure within Konoha who doesn't want Naruto to leave and become an independent force. He secretly sends assassins after Naruto. When Temari gets involved, this figure also targets her. His actions are driven by his thirst for power and fear of Naruto's potential outside of Konoha's control.
The elders of Konoha could be the main antagonists. They might be the ones who have been neglecting Naruto all along, and when he leaves, they see him as a threat to Konoha's stability.
It could be a rogue ninja from another village who has a vendetta against Naruto. This ninja might spread false rumors about Naruto in Konoha, which eventually leads to Naruto leaving. So, this ninja would be the main antagonist as he is the root cause of Naruto's departure.
Sasuke could also be the main character. Given his connection to powerful eyes in the Naruto series, if the Rinnegan was abandoned, Sasuke's role would change significantly. He would have to re - evaluate his own power and place in the ninja world, which could make for a really interesting story with him as the main focus.
It could be an unknown Uchiha who was overlooked in the main story. Maybe they were born with the Rinnegan but due to some political unrest in their village, they were forced to hide their power and were thus neglected. In the fanfiction, they could come out of hiding and shock everyone with their Rinnegan - based abilities.
His journey could lead him to the outskirts of the ninja world, to places that are unknown and full of mystery. With the Rinnegan, he might be able to access hidden paths or dimensions. He could be exploring these uncharted areas to gain more power and understanding, away from the politics and rules of Konoha.