Perhaps Naruto goes to Orochimaru in an attempt to redeem him. Naruto has a strong belief in the good in people, and he might think that he can convince Orochimaru to stop his evil ways. He could offer Orochimaru a chance at redemption, like a new start in the Hidden Leaf Village if he gives up his dark experiments and ambitions. This would lead to a complex relationship development between them, with Orochimaru being skeptical at first but gradually considering Naruto's offer.
Obviously, Naruto and Orochimaru are the main characters. Naruto is the protagonist who is going to Orochimaru, and Orochimaru is the one Naruto is going to see.
Well, in such a fanfic, Naruto joining Orochimaru would be a huge shock to the Naruto -verse. Orochimaru has always been an enemy, so for Naruto to side with him would mean a major shift in the power dynamics. Naruto could learn a great deal about the darker side of the ninja world, but he'd also be in constant danger of being used by Orochimaru for his own purposes. It would be a very different Naruto story, full of moral dilemmas and unexpected alliances.
In some fanfictions, Naruto might go to Orochimaru seeking power. He could be tempted by Orochimaru's knowledge of jutsu. Maybe he thinks that by learning from Orochimaru, he can become stronger faster and be better able to protect his friends and the village.
Well, Naruto might gain a lot of power quickly. Orochimaru has a vast knowledge of jutsu and forbidden techniques. However, he would be in constant danger. Orochimaru could be using Naruto as a pawn for his own goals, like taking over Naruto's body. Also, the power Naruto gets might be unstable or come with a price, like draining his life force over time.
In some fanfics, Naruto might use his new and powerful jutsu that he has mastered over time. Maybe he combines his Sage Mode with the power of the Nine - Tails in a unique way that Orochimaru can't counter. For example, he could use the Nine - Tails' chakra to enhance the range and power of his Sage Mode attacks, and then catch Orochimaru off - guard.
One consequence could be a shift in the power balance among the ninja villages. Since Orochimaru was a powerful and feared figure, his death might cause some chaos as his former allies or subordinates try to either avenge him or claim his resources. For example, some of his secret labs and experiments might be up for grabs, leading to potential conflicts.
A plot twist might be that Naruto and Sasuke discover a hidden agenda Orochimaru has that involves someone they care about deeply. For example, they find out he's planning to use Sakura as a sacrifice for some dark ritual. This would force them to quickly come up with a plan to rescue her and stop Orochimaru once and for all.
In fanfic, anything can be possible, so Orochimaru could be Naruto's father. But in the official Naruto storyline, it's not the case. Naruto's parentage is clearly defined as Minato and Kushina. Fanfic writers might be trying to explore a different kind of family drama or a new take on the characters' relationships by creating this unorthodox connection.
One possible fanfic could be about a student of Orochimaru who rebels against his evil ways. This student, perhaps having seen the destruction Orochimaru causes, decides to use the knowledge he has gained in a positive way. He might start by secretly helping the Hidden Leaf Village, using his skills in jutsu and forbidden arts to protect rather than harm.