It could be something like James, after Harry's father. It would be a way to honor his family's legacy.
They might choose a more unique name like Orion. It has a magical and celestial feel to it, fitting for a wizard in a world full of magic and mystery.
One possibility could be that their son inherits both Harry's courage and Hermione's intelligence. He might face new threats at Hogwarts, perhaps a new dark wizard rises. He could use his parents' knowledge and skills to outwit the enemy. For example, he might be great at Defense Against the Dark Arts like Harry and also be a top student in all academic subjects like Hermione.
His name could be Kazuki. It has a strong and modern feel to it, while still fitting in the Naruto universe. It could also mean 'harmony' or 'peace', symbolizing the hope that Sasuke and Sakura have for their family and the ninja world.
His magical abilities could develop in a more gradual and mysterious way. He might have dormant powers that only surface when he's in great danger or when he has a strong emotional connection to something. For example, he could discover he has the ability to communicate with magical creatures on a deeper level, like Harry could with snakes, but this power might not show up until he's older and has had certain experiences. Also, his magic could be influenced by the strong bond between Harry and Sirius, which could give him an edge in defensive magic.
His relationship with his parents could be very close. Since it's their son, Harry and Hermione would be extremely protective. They might also be a bit overbearing at times, trying to understand and manage his soul - bond. But overall, they would be a great source of support for him, using their own experiences in the wizarding world to guide him through any difficulties related to the bond.
It could be stronger in certain dark arts. Given his parentage, he might have a natural affinity for curses and hexes that are associated with the dark side. He could learn and perform these spells with greater ease compared to other wizards. However, he might struggle with defensive and positive magic, like healing spells or protective charms.
Harry might express his jealousy by being short - tempered around Krum. For example, when Krum tries to talk to him about Hermione, Harry could give curt responses.
He would probably be more conflicted. On one hand, he would have the potential for great good, like the original Harry. But on the other hand, he would have the shadow of Bellatrix's dark deeds hanging over him. This internal conflict could make him more withdrawn at times. He might also have a fascination with the dark arts, not in an evil way, but more out of a need to understand his mother's world. This would set him apart from the Harry we know, who was always more firmly on the side of light magic.
They would raise him with strong moral values. Given their own experiences, they would teach him about the importance of standing up against evil and the value of friendship. Harry would likely pass on his Quidditch skills and love for the sport, while Hermione would ensure he has a great education in magic.
It could be really interesting. Maybe Cora has some special powers or a unique background that she passes on to Harry. This could change the way he approaches magic and his adventures at Hogwarts.
The White Walkers could be major antagonists. They are a huge threat in Westeros and Harry and Hermione would have to use their unique magical abilities to combat them. Their cold - based magic and army of the undead would be a great challenge for Harry and Hermione.