Ron and Hermione become even more protective of Harry. They are constantly by his side, trying to cheer him up. Their relationship with Harry deepens as they share his pain. In some fanfictions, this brings Ron and Hermione closer together romantically as well, as they bond over their shared concern for Harry.
He becomes more withdrawn. Harry was always a bit guarded, but now he's even more so. He doesn't open up as easily to new people or even his old friends sometimes. He's also more determined. The loss of Sirius makes him more resolute in his fight against Voldemort, as if he has a personal vendetta now more than ever.
One common change is that he becomes moodier. The loss of Sirius is a huge blow, and he may swing between being extremely sad and angry. Another change could be that he is less likely to take risks without thinking. Sirius' death makes him more cautious as he realizes the consequences of recklessness.
Neville Longbottom could also play a more prominent role. Neville has his own growth arc in the series, and after Sirius's death, he could bond more with Harry over their shared experiences of loss. They could support each other in their fight against the Dark Arts. And perhaps some of the Death Eaters who were involved in Sirius's death could be main characters from the antagonist side, as Harry tries to track them down and bring them to justice.
In some fanfictions, Harry becomes more determined to fight against Voldemort. He channels his grief into training harder and becoming a stronger wizard. He often has flashbacks of Sirius which fuel his anger towards the Death Eaters and Voldemort, seeing them as the root cause of his loss.
One possible storyline could be Harry's struggle with his newfound loneliness and how it affects his magic. He might start to isolate himself more from his friends at Hogwarts, fearing that he'll lose them too. Another could be Harry's determination to avenge Sirius by seeking out the Death Eaters responsible for his death more aggressively.
If Naruto was Harry's father in the fanfiction, the story's power dynamics would shift. Naruto is used to dealing with threats on a large scale in his own world. He would bring that experience to the fight against Voldemort. Instead of relying solely on the Order of the Phoenix, Naruto might form his own group of allies, including some ninja - like characters he brings from his world. Also, Harry's understanding of loyalty and friendship would be deeper. Naruto values his friends above all else, and he would instill that in Harry from a young age, which could lead to different decisions in the story.
Harry's character would be more conflicted. On one hand, he has his natural inclination towards good from his original Potter bloodline. But on the other hand, Zeref's upbringing would expose him to darker elements. So he would constantly be at war within himself about what is right and wrong. For example, he might be tempted to use more aggressive or unethical magic to achieve his goals, yet still have that inner voice telling him it's wrong. Also, he would be more secretive, not sharing his thoughts and plans easily with others, as Zeref is often a rather mysterious character himself.
If Harry isn't the Boy Who Lived, it might mean a shift in the power dynamics within the wizarding world. Different characters could rise to prominence and the plot could take unexpected turns. Also, Harry's relationships with others might change as his status is different.
After Sirius dies, Harry is in a really tough place. He feels like a part of his family has been ripped away. He may start to question his own actions that led to Sirius being in the Department of Mysteries in the first place. Harry will also feel a sense of loneliness, even with his friends around. But over time, he'll remember the lessons Sirius taught him, about being brave and standing up for what's right. This will give him the strength to move forward, and he'll use his memories of Sirius as a source of motivation in his fight against Voldemort.
His sense of adventure might be different. In Narnia, he would be dealing with things like talking beavers and magical forests from a young age. So his idea of adventure would be more Narnian - themed. He might be more in touch with nature compared to his Hogwarts self.