It could be Orochimaru. He has always been interested in powerful abilities like the Sharingan. In this fanfiction, he might try to steal Naruto's newly acquired Sharingan for his own experiments and to increase his power even more.
One idea could be that Hatake Kakashi somehow transfers his Sharingan to Naruto in a dangerous mission. This would give Naruto new abilities and a whole new set of challenges to face. He'd have to learn to control the Sharingan quickly while also dealing with the enemies who might target him specifically for it.
In fanfiction, Naruto could get the Sharingan through a blood - related connection that is revealed later. For example, it could be discovered that he has some distant Uchiha ancestry that gets activated somehow. Maybe a powerful enemy's attack awakens this dormant Uchiha blood in him, and as a result, he develops the Sharingan. It could also be that a powerful sage or a new character uses their own unique powers to bestow the Sharingan upon Naruto for a specific purpose.
If Naruto had the Sharingan in fanfiction, it would likely lead to some interesting power - up scenarios. He could combine the power of the Sharingan with his own massive chakra reserves. This might make him an even more formidable opponent. His training would also take a new turn as he'd have to learn to control and master the Sharingan's abilities, like the different levels of the Sharingan and their unique powers.
Naruto might adapt by first trying to understand the basic functions of the Sharingan. He could start with the simple ability to see chakra flow more clearly. Since he has always been perceptive about people's emotions, he could use the Sharingan to read the emotions of his enemies through their chakra, which would help him in battles.
In this fanfiction concept, it could bring a whole new dynamic to the Naruto universe. Kakashi having Naruto as a son would mean a different kind of training for Naruto. Kakashi's calm and strategic mind could shape Naruto in unique ways. Maybe Naruto would inherit Kakashi's love for reading, especially those naughty books, and it could add a comical touch to his character while still maintaining his determination to become Hokage.
A prevalent theme is the exploration of his ninja skills. Writers often come up with new jutsus or ways for Kakashi to use his existing skills in more creative ways. Also, the theme of family is quite common. Given his father's story, fanfictions may explore how Kakashi views family and his place in it.
One drawback could be the strain on his body. The Sharingan is a powerful dojutsu, and Naruto's body, which is used to his own chakra system, might not be able to handle it well at first. This could lead to fatigue and over - exertion during battles.
In this fanfiction concept, Naruto and Sasuke as brothers could lead to a very different Naruto universe. With Sasuke having the Sharingan, he could potentially use it to protect Naruto more often. Maybe they would train together in new ways, combining Sasuke's Sharingan - related jutsu with Naruto's Uzumaki power. For example, Sasuke could use his Sharingan to analyze Naruto's chakra flow and help him master new forms of the Rasengan faster.
Yes, in some fanfictions, Naruto is given the Sharingan. Fanfiction writers often like to play with the concepts and powers in the Naruto universe, and giving Naruto the Sharingan can lead to some really interesting storylines. It might be a result of some kind of power transfer or a unique plot device.