Well, the character might become more confident, or perhaps overconfident. The power of the Rinnegan can be overwhelming, and they might start to think they're invincible. For example, they could become more reckless in battles, taking on stronger opponents without proper planning.
Another aspect could be the reaction of the other characters in the Naruto universe. Some might be fearful of the new power, thinking the character with the transplanted Rinnegan could become a threat. Others might see it as an opportunity to use this new - found power for their own purposes, like fighting against a common enemy. There could be a lot of political intrigue and power struggles within the ninja villages as a result.
One possible outcome in a Byakugan transplant fanfiction could be that the character who receives the Byakugan gains new abilities and a different perspective on the ninja world. For example, if Naruto were to receive a Byakugan transplant, he might be able to combine his existing Rasengan techniques with the long - range vision and predictive abilities of the Byakugan. This could make him an even more formidable opponent. He could detect hidden enemies from afar and launch surprise attacks with greater precision.
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.
In a Rinnegan Naruto The Originals fanfiction, the story could focus on Naruto exploring the true origins of the Rinnegan. He might discover that the Rinnegan has a connection to his Uzumaki heritage that was previously unknown. This could lead to a whole new arc where he has to travel to different hidden villages or ancient ruins to uncover more about this powerful eye technique and how it relates to his family's past.