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.
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.
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.
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.
Their relationship could become stronger. Facing the danger that Orochimaru represents together would force them to rely on each other more. They might start to understand each other's motives and fears better.
It would likely become more complicated. Sasuke has his own history with Orochimaru. If Naruto goes to Orochimaru for power, Sasuke might see Naruto as a rival in a different way. He could be jealous that Naruto is getting power from Orochimaru, or he could be angry that Naruto is making the same 'bad' choice he once did.
If young Orochimaru goes to Hogwarts in a fanfiction, it would be a really strange mix of two very different magical worlds. He would likely be fascinated by the magic taught there, but also might try to twist it to his own ends. For example, he could attempt to combine the magic of Hogwarts with his own ninja techniques. And he'd probably form some interesting relationships, either being feared or befriending some of the more adventurous students who are intrigued by his different approach to magic.
Well, in some versions, Naruto might use his new and improved Rasengan techniques. He could have combined it with his Sage Mode powers to overpower Orochimaru. Maybe he also uses his quick thinking and the element of surprise, since Orochimaru is always so full of his own schemes.