Sasuke might be the first to discover it. Since they are rivals and friends, he would be very attuned to Naruto's changes. Sasuke has his Sharingan which can detect power differences, so he could sense the new power of the Rinnegan within Naruto.
It could be Hinata. She is always observing Naruto from afar. One day, when Naruto is using his chakra in a new and different way, she might notice the unique pattern of the Rinnegan and figure out that he has this new power.
In fanfiction, Naruto might keep the Rinnegan a secret by avoiding using its powers in public. He could also use his shadow clones to create distractions when he feels like the Rinnegan is about to be revealed. Plus, he could tell only a very few trusted people, like Kakashi or Iruka, and ask them to keep it a secret for him.
Well, it could make Naruto extremely powerful right from the start. With the Rinnegan, he might be able to master all types of jutsu more quickly. He could also have an edge in battles against powerful foes like Madara or Kaguya. Maybe he'd be able to use the six paths techniques with more ease and less training.
A 'naruto secret rinnegan fanfic' might center around the idea of a hidden Rinnegan technique. In this fanfic, the author could be exploring how a character obtains the Rinnegan in a very different and secretive way compared to what we've seen in the official Naruto story. It could also look at how the Rinnegan interacts with other unique abilities in the Naruto universe, perhaps creating new and unexpected combinations of powers.
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.
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.
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 could completely change the power dynamic in the story. Naruto with the Rinnegan would likely become almost invincible, making his battles much less challenging.
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.
Well, there's a fanfic called 'Naruto's Rinnegan Adventure'. In this story, Naruto discovers the Rinnegan early on and has to deal with the consequences. It's interesting as it shows how his relationships with his friends and the village change due to this new power. Also, 'Rinnegan - Naruto's New Path' is a good one. It follows Naruto as he uses the Rinnegan to reshape the ninja world, facing many challenges along the way.