Naruto's view of justice could shift. With the Rinnegan, he would have access to new knowledge and perspectives. He might start to question some of the traditional ways of the ninja world and strive to create a more radical form of peace, which could be both good and bad depending on how it's executed.
He might also become more isolated at first. The power of the Rinnegan could make him feel different from his friends. He may think that they can't understand what he's going through with this new power, so he could withdraw a bit until he learns to balance his new abilities with his old relationships.
His character would have a darker edge. The vampire nature could bring out a more primal and possessive side. And the Rinnegan would give him new levels of power and knowledge. He might start to question his old values as he realizes the potential of his new powers. He could become more solitary, training alone to master his combined abilities rather than relying on his friends like he used to.
In the wider ninja world, his relationship with other villages would change. Some villages might see him as an even greater threat now that he has the Rinnegan, and might try to form alliances against him. However, Naruto being Naruto, he would use his new power to show that he still has the same kind - hearted goals. He would try to use the Rinnegan to bring about peace even more strongly, and over time, win over those who were initially suspicious.
If Naruto got the Rinnegan, he might become more cautious. The power of the Rinnegan is so great that he would realize he needs to be more careful with it. He wouldn't be as brash as before.
He would likely become more brooding. With the dark and godlike Rinnegan, Naruto might start to question his previous beliefs. He could be more isolated as he tries to figure out his new power, which is different from the chakra he's used to. His usual sunny and optimistic personality might be overshadowed by a more serious and cautious side.
Naruto would likely become more confident in battle. With the Rinnegan, he has access to new and powerful techniques. This would change his fighting style and make him bolder in combat situations. He may also start to take on more leadership roles as others recognize the power of his new - found ability. For example, he could lead more complex and dangerous missions. Moreover, his relationships with some characters might change. Some who were once his equals in power might now look up to him more, which could create new dynamics in his friendships and alliances.
His combat style would change drastically. Instead of relying solely on ninjutsu, he'd be using the powers of the Lantern Ring. For example, if he had a Blue Lantern Ring, which is associated with hope, his attacks would be filled with a sense of optimism and might even inspire his comrades in battle more than before. His enemies would be facing a very different Naruto, one with powers that they may not have any prior knowledge of how to counter.
Their relationship would likely become more complex. With the Rinnegan involved, they might have to rely on each other more for understanding its powers. They could become more protective of each other, knowing the power and the danger it brings.
Well, for starters, his power progression would be completely different. Without parental support, he'd have to figure out the Rinnegan's abilities all by himself. Maybe he'd accidentally unlock some dangerous powers early on because he didn't have anyone to guide him. His emotional state would also be a mess. He'd probably be angry at his parents for neglecting him and use that anger as fuel to train harder.
If Naruto had both in fanfiction, he'd be insanely powerful. His combat abilities would skyrocket. He could use the Sharingan to quickly analyze his opponents' moves and the Rinnegan to counter with powerful six - paths techniques. For example, he could use the Sharingan to predict an enemy's attack and then use the Rinnegan's Deva Path to repel it with ease.
Well, at first it might cause some strain. His sister may feel overshadowed by Naruto's new power. But as time goes on, Naruto could use the Rinnegan to help his sister discover her own latent abilities. This would transform their relationship into one of mutual growth and support. He could use the powers of the Rinnegan to train her in unique ways, and she could in turn offer him emotional support, making their bond even deeper than before.