In some fanfictions, Naruto might get the Rinnegan from Nagato through a transfer of power. This could be due to Nagato seeing Naruto as a worthy successor and using some sort of jutsu to pass on the Rinnegan's power before he dies. Another possibility is that there is some sort of magical or spiritual connection between them that enables the transfer.
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.
In some fanfictions, Naruto might get injured by Nagato's powerful jutsus. For example, Nagato could use his Chibaku Tensei in a more unexpected way, catching Naruto off - guard and causing him physical harm. Maybe Naruto tries to approach Nagato too quickly to reason with him and Nagato, in a split - second decision, uses a blast of Shinra Tensei to push Naruto back, resulting in Naruto getting injured as he crashes into surrounding debris.
The Rinnegan would supercharge Naruto's abilities. Naruto already has a vast amount of chakra and with the Rinnegan, he could use that chakra in more diverse and powerful ways. He might gain the ability to use the Deva Path's power to manipulate gravity, which could be used both defensively and offensively. His Sage Mode combined with the Rinnegan could create a whole new level of fighting style, allowing him to quickly assess and counter his enemies' moves more effectively.
It would change his abilities in multiple ways. Firstly, with the Rinnegan, Naruto could have better perception of the world around him, similar to how Nagato was able to sense things from afar. Secondly, he might be able to use the Animal Path to summon powerful creatures. This would give him more options in battle. Also, the Rinnegan could potentially allow Naruto to access some form of chakra absorption or manipulation that he didn't have before, further diversifying his power set.
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.
The story would change drastically. Naruto's combat abilities would be enhanced. He could use the Rinnegan's powers like the Six Paths techniques, which would give him an edge in battles. For example, he could use the Preta Path to absorb chakra attacks from opponents.