Naruto's view of family would expand greatly. He has always been seeking acceptance and a sense of family. With Kurama as his sister, he now has a family member who is part of his very being. This could make him more empathetic towards others who are also searching for family. He would be more likely to reach out and help those in need, based on his own experience of finally having a true family connection in Kurama.
Naruto would have a different relationship with the other villagers. With Kurama's influence, he might be more aloof or even feared at first because Kurama is a tailed beast. But as he grows, he could use this to his advantage to break down the barriers between the villagers and the tailed beasts. He would be more of an advocate for understanding and co - existence, which would be a significant shift from his regular character development where he was mainly focused on becoming Hokage to gain the villagers' respect.
He would be more confident. Without the constant internal struggle with Kurama, Naruto would have a more stable mental state. He could focus more on his ninja goals and less on suppressing Kurama's negative influence.
Naruto might become more conflicted. Since Madara had some extreme views, Naruto would have to grapple with those ideas. He could become more secretive as he tries to understand Madara's motives better without alarming his friends. For instance, he might start training alone more often to study Madara - inspired techniques.
In the 'kurama is naruto's little sister fanfiction', Kurama's character may lose some of its wild and untamed nature. She could become more empathetic and in tune with human emotions, similar to how a sister would be. For instance, she might be more sensitive to Naruto's feelings and experiences. In the original series, Kurama was often more of a force of nature, but as a sister, she'd have a closer, more emotional bond with Naruto, leading to a significant shift in her overall character.
If Sasuke's sister was in the picture, Naruto and Sasuke's relationship might soften more quickly. Naruto would see another side of Sasuke through his sister. He might also feel more of a connection to Sasuke's family. Sasuke, on the other hand, would see Naruto's genuine care for his sister, which could make him trust Naruto more.
Their relationship might become stronger. In the past, Naruto could show Kurama that he is more than just a host, and Kurama could see Naruto's potential to change things even at an earlier stage.
Naruto being raised by Sasori would be a huge shift. Sasori is not one to show much emotion or promote the ideals of hope and perseverance like the people in Konoha. Naruto would likely have a different sense of loyalty, perhaps more towards Sasori's goals or ideals which are mainly centered around his own power and the art of puppetry. His growth as a ninja would be more focused on silent and deadly skills rather than being a hero that everyone looks up to. His relationships would be more transactional in nature as he wouldn't have been exposed to the deep emotional bonds that are so prevalent in Konoha.
If Naruto was raised by Vegeta, his character would likely become much more aggressive and focused on power. Vegeta's Saiyan pride and his constant drive to be the strongest would rub off on Naruto. He might not be as friendly or as empathetic as in the original series, but would instead be more solitary in his pursuit of strength, seeing it as the ultimate goal.
It would likely accelerate his growth. Jiraiya is a very experienced ninja. With his guidance, Naruto would gain more confidence. For example, if Jiraiya found Naruto early on, he could teach Naruto better control of his chakra, which was a struggle for Naruto in the beginning. This would make Naruto more efficient in battles and less reliant on brute force.
Naruto would likely become more disciplined. Kakashi is known for his strictness, so Naruto would have to follow a more structured training regime. This would make him more focused during battles and in his studies of ninjutsu.