Naruto's character might develop a stronger sense of purpose. Saving Sasuke becomes more than just about their friendship; it could be about righting a wrong in the ninja world. His resolve to save Sasuke would make him train harder and become more strategic in his battles.
His character could develop in terms of his understanding of the darker side of the ninja world. Facing Orochimaru to save Sasuke exposes Naruto to the kind of evil that exists. This makes him more empathetic towards those who have been influenced by such evil, like Sasuke. He may also learn new jutsu and techniques in his journey to save Sasuke, which further enhances his skills and confidence as a ninja.
Naruto's character could develop a deeper sense of protectiveness. Saving Sasuke makes him more aware of his feelings towards her and how important she is to him. This might lead to him being more cautious in battles and thinking more about the consequences of his actions as he doesn't want to put Sasuke in danger again.
In some fanfictions, Orochimaru might develop a sense of loyalty towards Naruto. After being around Naruto for a while, he could see Naruto as someone worthy of his loyalty. This could lead to him being more open to working with the Hidden Leaf and helping Naruto in his various missions. He might even sacrifice his own interests to protect Naruto at times, which is a complete turnaround from his initial character.
Naruto's character could develop a deeper sense of responsibility. Saving Konan from Obito would show that he is not only protecting his close friends from Konoha but also those from other villages. This would expand his view of what it means to be a hero.
Naruto's character could develop in terms of his leadership skills. When he saves Neji, he has to take charge of the situation, making quick decisions on how to deal with the threat to Neji. This would show his growth from the impulsive boy to a more responsible leader. He might also develop more empathy as he realizes the pain and danger Neji is in, which further deepens his bond with his comrades.
His character could develop by becoming more nurturing. When he saves the child, he realizes the importance of protecting the innocent. So, he might become more cautious in his actions to avoid endangering others.
Naruto's character develops by becoming more empathetic. He starts to understand the pain and loneliness of the Bijuu. This makes him less impulsive and more strategic in his approach to saving them. He also grows in terms of his leadership skills as he has to convince the Bijuu to follow him.
Perhaps in this fanfiction, Naruto has some sort of special power or transformation that he unlocks just in time to face Orochimaru. It could be related to his Nine - Tails chakra in a new and unique way. He uses this power to break through Orochimaru's defenses and save Hiruzen. Naruto might also use his knowledge of Orochimaru's weaknesses that he has learned either from Jiraiya or from his own past encounters with Orochimaru's minions.
Naruto's character could develop in terms of his strategic thinking. Since saving Gaara from the Akatsuki is no easy feat, he might have to come up with more complex battle plans. This would show his growth from a brash fighter to a more calculating ninja.
After saving Sakura, Naruto would probably become more mature. He realizes that his friends can be just as vulnerable as he once was. This experience would make him more patient. He would no longer just jump into action without considering the emotional state of others. His relationship with Sakura would also change. It would be deeper and more complex, and this new dynamic would force him to grow as a person. He might start to study more about mental health in the ninja world, so he can better prevent such situations in the future.
Sasuke's character often develops in terms of his loyalty. By saving Naruto, he shows that his loyalty to their friendship is growing stronger. He may start to question his previous lone - wolf attitude.