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.
One implication is that he becomes much more powerful. The Rinnegan gives him access to powerful abilities like the Six Paths techniques, which would change the power dynamics in battles in the fanfiction. He could now face stronger enemies more easily.
In some fanfictions, Naruto might awaken the Rinnegan through a powerful jutsu overload. For example, if he combines a super - charged Rasengan with some ancient and forbidden chakra - based techniques. This could potentially trigger a genetic or chakra - system shift that results in the awakening of the Rinnegan.
In some fanfictions, Naruto might awaken his Rinnegan through a powerful and ancient jutsu. For example, he could come across a hidden scroll that contains the knowledge and power to unlock this dojutsu. Maybe a mysterious sage or an old shinobi reveals the secret to him, guiding him through a series of trials that eventually lead to the awakening of the Rinnegan.
Well, in certain fanfictions, Naruto's view of the ninja world as a whole can shift after the Wave arc. He might start to question the traditional ninja values. Since he witnessed the greed and corruption that led to the problems in Wave, he could strive to change the ninja world from within. He may begin to form his own ideas about what it truly means to be a ninja, which could be different from what he was taught at the academy. He could try to promote peace and cooperation more actively, rather than just following orders blindly.
In some fanfictions, Naruto might become more strategic during the Wave arc. He could learn from his mistakes faster and start to think several steps ahead in battles, instead of just charging in blindly like he sometimes does in the original story.
When Naruto awakens Mokuton in the Wave fanfiction, his role in the Wave mission is transformed. Mokuton is a powerful and versatile ability. Naruto could use it to camouflage the group by creating a forest - like environment, making it harder for the enemy to find them. He could also use wooden constructs to hold off attackers while the others carry out the main objective of the mission. This new power elevates his status from a novice ninja trying to prove himself to a crucial part of the mission's success.
One potential antagonist could be Orochimaru. He is always after powerful jutsus and the power of the Rinnegan would be extremely appealing to him. He might try to either steal Naruto's newly awakened Rinnegan or prevent Naruto from fully mastering it so that he can be the most powerful one in the ninja world.
In such a fanfiction, Naruto might gain incredible new powers. He could potentially use the Rinnegan's abilities like the Six Paths techniques. This would likely change the power dynamics in the Naruto universe completely, making him an even more formidable opponent against enemies.
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.
In some fanfictions, it could be due to a powerful emotional shock. Maybe seeing a friend in great danger at Wave, like Sasuke almost dying, could trigger an unexpected connection to the Sharingan. Since Naruto has a strong bond with Sasuke, this extreme situation might force his latent Uchiha - like powers (in the context of the fanfic) to surface, awakening the Sharingan.