His character may become more withdrawn at first. Losing Jiraiya, who was like a father figure to him, could make Naruto less open and more focused on his internal pain.
One possible scenario could be that Naruto leaves to train in isolation. He might feel that he needs to become stronger on his own without the guidance of Jiraiya, and so he sets off to find new ways to improve his skills.
The training makes Naruto more confident in his abilities. Jiraiya constantly challenges Naruto and as Naruto overcomes these challenges, he realizes his own strength. He starts to believe in himself more, which is evident in the way he faces stronger opponents without hesitation later on. Also, Jiraiya's teachings about the ninja way and the importance of protecting those you love make Naruto more determined and focused on his goals.
Their relationship would be very strong. Jiraiya would see Naruto as not just a student, but also as a connection to Minato. He would be strict but also very affectionate. Naruto would look up to Jiraiya as a father figure, since he never really had one. They would share many adventures together, with Jiraiya teaching Naruto about life, love, and ninjutsu.
It can create a sense of growth for Naruto. Without Jiraiya by his side, he has to rely more on his own instincts and the skills he has already acquired. This can lead to new character development as he faces challenges alone.
Jiraiya's training in the fanfiction might focus on Naruto's inner strength as well. He could help Naruto better understand and control the Nine - Tails' power. This new - found control would give Naruto a sense of calm and authority. His character would shift from being just a loud - mouthed underdog to a more respected and powerful ninja. Naruto would also learn about loyalty and sacrifice from Jiraiya, which would shape his values.
It could be Orochimaru. Since Orochimaru has a long - standing feud with Jiraiya and is always up to no good. If Naruto ditches Jiraiya, Orochimaru might see this as an opportunity to manipulate Naruto. He could try to convince Naruto that Jiraiya was holding him back and that he can offer Naruto more power, all while having his own evil plans for Naruto.
Jiraiya might comfort Naruto by sharing his own experiences. He could tell Naruto about the times he faced difficulties and how he overcame them. For example, he might talk about his training with the toads and how he grew stronger through perseverance.