Regarding the characters who possess the Rinnegan in the original and the fanfic, there are differences. In the original, we mainly see characters like Nagato and Sasuke with the Rinnegan. In the fanfic, new characters might be introduced with the perfect Rinnegan. These characters could have different relationships with other Naruto characters and different goals, which can significantly change the overall narrative compared to the original story.
It could also be a situation where Naruto's connection to Hagoromo is deepened in the fanfiction. For instance, Naruto might have a vision or a spiritual encounter with Hagoromo. During this encounter, Hagoromo realizes that Naruto is the key to bringing true peace to the ninja world. So, he imparts the power of the Rinnegan to Naruto to help him achieve this grand goal. This would be a more complex and involved process, perhaps involving Naruto learning about Hagoromo's past and his own role in the grand scheme of things.
In some fanfictions, it could be through a strange and powerful jutsu transfer. Maybe Madara, on the verge of defeat, decides to transfer his Rinnegan power to Naruto for some unforeseen reason, like seeing a new path for the ninja world in Naruto.
In some fanfiction concepts, the chakra of the Kyuubi is not just pure fox chakra but also contains remnants of the Sage of Six Paths' power. Since the Rinnegan is related to the Sage of Six Paths, when Naruto reaches a certain level of power and harmony with the Kyuubi, the dormant Rinnegan - like power within the Kyuubi's chakra awakens in Naruto. This could be a result of Naruto's strong will and his journey to master the Kyuubi's power which eventually leads to him obtaining the Rinnegan.
He could become more confident, bordering on overconfident at times. With the Rinnegan, he has access to incredible powers, and this newfound strength might make him believe that he can handle any situation alone. However, his friends would surely keep him in check. For example, he might initially rush into a battle thinking his Rinnegan - enhanced abilities will ensure victory without fully considering the risks, but then realize his mistake when his friends point it out.
Another possibility is that it's a result of some strange chakra experiment gone wrong (or right). Scientists in the Naruto universe are always dabbling in chakra research. Maybe an experiment meant to enhance her natural abilities instead gives her the Rinnegan, and she then has to learn to control it quickly to avoid being consumed by its power.
It might be related to a connection with some powerful entity in the Wave arc. For example, if there's a secret shinobi from the past whose power is tied to the Rinnegan and Naruto somehow forms a bond with that power source, it could lead to the awakening. Also, the intense emotions and challenges he faces in the Wave arc might be a catalyst, pushing his chakra to a new level and awakening the Rinnegan.
In some fanfiction concepts, it might be due to a unique chakra interaction. Maybe the Kyuubi's powerful and ancient chakra somehow triggers a latent ability within Naruto that results in the manifestation of the Rinnegan. It could also be part of some kind of prophecy or destiny within the fan - created world of the story.
One possibility is that there was some sort of spiritual or chakra - based connection between Naruto and Nagato. Nagato, being the possessor of the Rinnegan, recognized Naruto's strong will and the fact that he was on a path to change the ninja world for the better. Through this connection, Nagato was able to transfer the power of the Rinnegan to Naruto. It could also be related to the nature of the Sage of Six Paths' power that was somehow involved in this transfer, as both Naruto and Nagato were related to the Sage in different ways.
In some fanfiction concepts, there could be a spiritual or mental connection established between Naruto and Nagato. Since Naruto has this unique ability to understand and connect with people on a deep level. Through this connection, Nagato might pass on the power of the Rinnegan to Naruto. It could be like a transfer of not just the physical power but also the knowledge and understanding that comes with the Rinnegan.
One interesting aspect could be the unique interpretations of the Rinnegan's powers. In fanfics, the author might explore new ways the perfect Rinnegan can be used in battles, like combining different jutsu in unexpected ways. For example, it could be used to manipulate time and space simultaneously, which is not seen in the original Naruto series. This adds a new layer of excitement and unpredictability to the story.