One common theme is trauma. Often, Naruto experiences some sort of extreme trauma that causes his personality to change. For example, in some fics, he witnesses the death of all his friends and becomes a cold and revenge - driven person.
Naruto's upbeat and positive personality would be a huge change. He's always been able to make friends easily, and in Hogwarts, he'd probably have a much wider circle of friends from different houses right from the start. This could lead to a more united Hogwarts against Voldemort. His never - give - up attitude would also be a big factor. When facing challenges like the Triwizard Tournament or dealing with Voldemort's threats, he wouldn't be as easily daunted as Harry was at times.
Well, with Minato's personality, Naruto would probably be more reserved in showing his emotions. He wouldn't be as boisterous or loud as he usually is. This could change his relationships too. For example, his interactions with Sasuke might be less about yelling out his feelings and more about subtly trying to understand and help him. Also, his leadership style could be more like Minato's, inspiring trust in his comrades through his composed and intelligent demeanor.
If Naruto had Gaara's personality, the story would be very different. Naruto is usually outgoing and boisterous, while Gaara is more reserved and initially cold. With Gaara's personality, Naruto might not be as quick to make friends. He'd be more guarded and less likely to trust others easily. This could change his relationships with characters like Sasuke and Sakura. His interactions with the villagers would also be different. Instead of trying to gain their approval through big shows of strength and determination, he might keep more to himself, which could slow down his journey to becoming Hokage.
If Naruto becomes involved with Slenderman in a fanfiction, his usually cheerful and determined personality might become darker. He could be more withdrawn as he grapples with the strange and often terrifying aspects of Slenderman's world.
Naruto's personality may not change drastically in terms of his fundamental values like loyalty and the pursuit of his dreams. However, as a girl, he might be more attuned to the social hierarchies among female characters. He could start to notice and react to the cattiness that might exist in some female - only groups in the village. This new awareness could add a layer of complexity to his interactions, but at the same time, he would still be the Naruto who wants to prove himself and protect the village at all costs.
He might become more brooding. Instead of his usual sunny and determined self, he could be more withdrawn as a dark cleric, constantly thinking about the implications of his new powers and the dark path he's on.
Naruto's personality might become more empathetic. As a female, he could be more in tune with the emotions of others around him. For example, he might be quicker to comfort a distraught friend.
His personality might become more refined. Instead of being the rowdy Naruto we know, he could be more composed and polite due to the influence of the daimyo's court.
Naruto might become more calculating. Urahara is a very strategic person, and under his training, Naruto could start thinking more before acting. For example, instead of just rushing into a fight, he'd analyze the situation first.