The story would likely focus more on Naruto's individual growth without Sasuke. He could start new friendships or focus more on his ninja skills. Also, Sasuke's story would take a different turn as he no longer has Naruto constantly on his tail. He might become even more isolated or find new allies who are not as positive as Naruto was.
The dynamic between Naruto and Sasuke would be completely different. Instead of the usual pursuit, there would be a sense of finality. Naruto might start to avoid Sasuke, which would change the way Sasuke views Naruto too.
The overall mood of the story would become darker. The hope that Naruto represented for Sasuke's redemption is gone. This could lead to more conflict in the ninja world as Sasuke may become more of a threat without Naruto there to try and bring him back. Other characters would also be affected, like Sakura who always hoped Naruto could save Sasuke. She might be disappointed and this could change her character development as well.
The story would take a very different turn. The dynamic between Naruto and the rest of the characters would change. For example, Naruto might become more focused on protecting the village without the distraction of Sasuke. His relationships with other friends like Sakura might also be affected. Sakura might be disappointed in Naruto at first for giving up, but then they could bond over the loss of Sasuke in a different way.
If Naruto gives up on Sasuke in fanfiction, the storyline could take a very different turn. For one, the whole dynamic of their relationship, which has been a central part of the original Naruto story, would be completely disrupted. Naruto has always been determined to bring Sasuke back to the village. Without that drive from Naruto, Sasuke might become even more isolated and perhaps fall deeper into the darkness. This could also lead to different power alignments in the ninja world. Allies of Naruto might question his change of heart, and enemies could take advantage of the rift between the two former friends.
If Naruto gives up his dream, Sasuke might view him as a weakling. Sasuke has always been competitive with Naruto, and Naruto's giving up could make Sasuke lose respect for him. Their relationship could become strained as Sasuke may distance himself from Naruto, thinking he is no longer the worthy rival he once was.
Well, it makes him more cynical. Normally, Naruto is a very positive and hopeful character. But in this fanfic, giving up on everyone would turn him into someone who doubts the goodness of people. He would become more withdrawn and less likely to reach out to others.
Well, if Sasuke gives Naruto his Rinnegan in fanfiction, Naruto's abilities would be greatly enhanced. The Rinnegan is extremely powerful, granting abilities like the Six Paths techniques. Naruto might gain better control over space - time, be able to use powerful gravitational and repulsive forces more effectively, and perhaps even access new forms of chakra manipulation. This could make him an even more formidable opponent, able to take on stronger enemies with ease.
Maybe Naruto gets tired of always chasing after Sasuke. He has his own life and dreams too. He might think that he has sacrificed enough of his time and energy on Sasuke, and it's time to focus on himself and the village. He could start to believe that Sasuke has made his own choices and he can't keep forcing Sasuke to come back.
He becomes more solitary. Without the pursuit of love, Naruto focuses more on self - improvement and his ninja skills. He might seem more aloof as he distances himself from the idea of a relationship. For instance, he spends more time training alone in the forest.
The story might take a more somber turn. Snape could become more withdrawn and focus solely on his own pursuits. For instance, he may throw himself into his potions research even more intensely.
The story could take a dark turn. Without his heart, Naruto might become a soulless being, and his friends would be devastated. They might try to find a way to get his heart back. Maybe they search for a powerful sage or some ancient magic that could reverse what has been done.
The relationship would become very tense. Naruto would likely avoid Sakura and Sasuke. There would be no more of the friendly banter or the complex emotional triangle that was there before. It's a complete shift from their normal relationships in the original story.