In the fanfiction, Naruto being taken by Orochimaru could lead to a whole new set of character developments. For one, Naruto's view of the ninja world might change. He's used to the relatively 'good - guy' environment of Konoha. But with Orochimaru, he'd be exposed to the more underhanded and cruel aspects of the ninja world. His relationships with his friends could also be put to the test. His friends would surely try to rescue him, and Naruto would have to decide whether to rely on them or try to handle things on his own while in Orochimaru's clutches.
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.
In a fanfiction where Naruto and Hinata join Orochimaru, one possibility is that they are forced into it. Maybe Orochimaru has some kind of leverage over Konoha that makes them comply. Naruto, being the head - strong character he is, would likely be constantly looking for a way to escape and take Hinata with him. Hinata, on the other hand, would probably be more reserved and observant, trying to find Orochimaru's weaknesses.
Well, if Naruto is captured by Orochimaru in fanfiction, one possibility is that Orochimaru wants to use Naruto as a bargaining chip against Konoha. He may think that by having Naruto in his grasp, he can force the Hidden Leaf to meet his demands, like giving him access to certain forbidden jutsu or secret scrolls. Another aspect could be Orochimaru's curiosity about Naruto's ability to master new jutsu so quickly. He might want to study Naruto's mind and body to find out the secret behind his growth as a ninja.
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.
In some fanfictions, Naruto might kill Orochimaru by overpowering him with newfound powers. For example, if Naruto has a sudden boost in his Sage Mode or a new jutsu he developed. Orochimaru is a powerful foe, but Naruto's growth could potentially lead to his defeat. Maybe Naruto has also mastered some sealing techniques that can counter Orochimaru's ability to regenerate and transfer his soul.
One possibility is that Naruto discovers Orochimaru's lair through some clever detective work. He then sneaks in, avoiding all the traps. When he sees Orochimaru about to perform some sort of experiment on Hinata, Naruto jumps in and starts fighting. He might transform into his Nine - Tails Chakra Mode to gain an edge in the battle and save Hinata.
The apprentice could learn unique jutsu from Orochimaru. Since Orochimaru is known for his forbidden jutsu, the apprentice might gain an edge in combat but also face the danger of being corrupted by the power. They could then use these skills in battles against common enemies. And, in the process, they might try to redeem Orochimaru in some way, like showing him that there is a better path than his thirst for power.
Naruto might learn some very dark and powerful jutsus. Orochimaru is known for his forbidden jutsu knowledge. So Naruto could become a much more dangerous fighter but also risk being influenced by Orochimaru's immoral ways.
In a fanfiction where Naruto is adopted by Orochimaru, Naruto's development would take a very different turn. Orochimaru could train Naruto to be more ruthless in combat. However, Naruto might also resist Orochimaru's darker intentions. This internal struggle could be a major part of the story. Naruto might try to find a way to use Orochimaru's knowledge for good, while still holding onto his own values. He could also face discrimination from other ninjas who see him as Orochimaru's apprentice and therefore a potential threat.
In fanfiction, if Naruto were trained by Orochimaru, he might gain some very dark and powerful jutsu. Orochimaru is known for his unethical experiments and forbidden jutsu. Naruto could become a more morally ambiguous character, as Orochimaru's influence might taint his usually positive and straightforward nature. His power level would likely skyrocket, but at the cost of his relationships with his friends in Konoha who might be wary of his new, darker abilities.