Well, Naruto might discover some new Orochimaru's plan during the rescue. Maybe Orochimaru was trying to use Hinata to get some information about the Byakugan. After saving Hinata, Naruto could go on a mission to stop Orochimaru from achieving this goal with the help of his friends like Sasuke and Sakura.
One possible plot development could be that after saving Naruto, Madara tries to mentor him. He sees Naruto's potential and wants to shape him into an even greater ninja, sharing his own knowledge and skills that have been honed over years.
One possible plot twist could be that Orochimaru was actually being controlled by a greater evil, and Naruto has to not only save Hinata but also deal with this hidden threat. Maybe Orochimaru was forced to target Hinata to draw Naruto out for this other entity's purposes.
One possible plot development could be Naruto's struggle to break free from Orochimaru's control. He might have to face his inner demons and find new sources of power within himself. Another could be his friends trying to rescue him and having to fight against Orochimaru's minions. Maybe Naruto under Orochimaru's control is used to target the Hidden Leaf Village, creating a huge conflict.
One possible plot development could be Naruto learning some of Orochimaru's unique jutsu. For example, he might pick up on Orochimaru's snake - related techniques. This could give Naruto an edge in combat against opponents who are not familiar with such unorthodox attacks. Also, Orochimaru's knowledge of forbidden jutsu might be passed on to Naruto in a modified, less dangerous way, which could then be used to surprise his enemies in future battles.
I'm sorry I haven't read a specific fanfiction with this exact plot, but generally in such a scenario, Naruto would probably use his powerful jutsu like Rasengan. He'd sense Hinata in danger from Orochimaru, rush to the scene, and engage in a fierce battle with Orochimaru to rescue Hinata. Maybe he'd also get some help from his friends along the way.
For Naruto, he could develop more in terms of his leadership skills. In fanfiction, he might learn to be more diplomatic when dealing with the different clans in Konoha, especially when working with Hinata's Hyuga clan. He would become more of a unifying figure, not just a powerful ninja.
Tenten could have a character development arc where she gains more recognition. In the original series, she sometimes seemed in the shadow of the more prominent characters. In fanfiction, she could be given more important roles in missions. She might also develop a unique fighting style that combines her weapon expertise with some form of elemental jutsu, making her a more formidable force in combat.
Naruto could also develop his diplomatic skills. Suppose there is a situation where the village needs to make an alliance with another village and Naruto, Hinata, and Hana are part of the diplomatic team. Naruto would have to learn how to negotiate and communicate effectively. Hinata could develop her ability to sense danger on a larger scale. Maybe there are threats to the alliance that she needs to detect. Hana could develop her ability to adapt to different environments. If they travel to another village for the alliance, Hana would need to adjust quickly and use her skills in new and unfamiliar situations.
One possibility is that Naruto's friends launch a rescue mission. They would use their unique skills, like Sasuke's Sharingan or Sakura's medical ninjutsu combined with her combat skills, to find and save Naruto.
One possible plot development could be Naruto struggling with Orochimaru's dark teachings while still holding onto his own sense of justice. Maybe he tries to find a way to use Orochimaru's knowledge for good. For example, he could learn some unique jutsu from Orochimaru and then modify them to be less harmful or more in line with Konoha's values.