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.
Well, Naruto could potentially be used as a bargaining chip by Orochimaru. Orochimaru might try to trade Naruto for something he wants from Konoha, like secret jutsu scrolls or some kind of political power within the village. And Naruto, being the determined hero he is, would likely be constantly looking for a way to escape and foil Orochimaru's plans.
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 use his Nine - Tails chakra to break free. He's a tough one. He could also try to outwit Orochimaru with his ninja skills. Maybe he'd pretend to be unconscious and then surprise Orochimaru when he least expects it.
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.
Naruto getting kidnapped by Orochimaru would be a really dangerous situation. Orochimaru could start by putting Naruto in some sort of chakra - suppressing device. This would limit Naruto's ability to use his Nine - Tails power. Then, he might try to implant some of his cursed seals on Naruto, which would give him more control over Naruto. But Naruto has his own allies within himself. The Nine - Tails, despite their rocky relationship, might help Naruto out in this situation. Also, Naruto has the memories of all the people who care about him. He'd draw strength from those memories and keep his hope alive, waiting for the moment when he can break free and return to his friends and the village.
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.
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.