Well, first of all, Naruto with the Rinnegan would be a total game - changer. In the story, the Rinnegan has always been associated with great power and mystery. If Naruto got it implanted, he could potentially use the Deva Path to manipulate gravity, which would be a huge advantage in combat. His enemies would have to completely re - evaluate their strategies against him. And on a more character - development level, he might struggle with the new power, as it comes from an external source and not his own natural growth. This internal conflict could add a whole new layer to his character arc.
One interesting aspect would be seeing Naruto combine his existing jutsu with Rinnegan abilities. For instance, mixing his Rasengan with the power of the Rinnegan's Six Paths could create an entirely new and devastating attack. Another aspect is how it would affect his relationship with Sasuke. Sasuke has the Sharingan and later the Rinnegan in the original story. With Naruto also having the Rinnegan, their dynamic would change, perhaps leading to new rivalries or alliances based on their shared power.
Maybe it's from a powerful villain. In some fanfictions, this could be a really interesting twist. The DNA of a villain like Orochimaru could give Naruto some of his snake - like abilities or his knowledge of forbidden jutsu. However, Naruto would then have to struggle with the darker instincts that might come with that DNA. Another possibility is that it could be from an ancient and powerful demon. This would bring out a whole new set of challenges and powers for Naruto to deal with.
Maybe Kabuto. He was Orochimaru's right - hand man and had access to a lot of his knowledge and resources. He was also involved in various experiments. Given Naruto's importance in the Naruto world, Kabuto might see the potential in implanting a Byakugan in him. It could be part of a larger scheme to gain an advantage in the ongoing power struggles in the shinobi world.
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 Naruto fanfiction, the Rinnegan in Naruto is often portrayed in really cool and powerful ways. Some fanfics might give Naruto the ability to use all the Rinnegan powers to their fullest extent right away, like being able to effortlessly summon the Gedo Statue or use the Deva Path powers without any drawbacks. It's a way for writers to explore new storylines and make Naruto even more of a badass than he already was in the original series.
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.
If Naruto got the Rinnegan, he might become more cautious. The power of the Rinnegan is so great that he would realize he needs to be more careful with it. He wouldn't be as brash as before.
Well, when it comes to Naruto time travel and Rinnegan in fanfics, it's often about exploring new storylines. Maybe Naruto himself gets the Rinnegan and travels back in time to train his younger self. This would make him a much more powerful ninja at an earlier stage and could completely change the power balance in the Hidden Leaf Village and among the other ninja villages as well.
There's a fanfic where the female Naruto gets the Rinnegan and teams up with some unexpected allies. This fanfiction focuses on her journey to understand the true nature of the Rinnegan and how it can be used to bring peace to the ninja world. It's a great read as it shows her growth from a young kunoichi to a powerful force with the Rinnegan.