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.
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 He could be more withdrawn as he grapples with the strange and often terrifying aspects of Slenderman's world.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 Instead of his usual sunny and determined self, he could be more withdrawn as a dark cleric, constantly thinking about the implications of his new powers and the dark path he's on.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.
In such fanfiction, Naruto's personality could be a mix of his old self and a new, more complex version. He would still be the determined and kind - hearted Naruto at heart. However, the power of the hollow mask might make him more secretive. He might keep things from his friends and mentors for fear of them trying to take the mask away. This internal conflict between his old and new self could be a major part of his character development.
If Naruto is pretending to be a girl, his normally boisterous and energetic personality might become more subdued at first. He'd have to be more careful with his actions and words to fit the female role. For example, he might not be as loud or impulsive as he usually is.
He might become more serene. Since Sadaiam might have a calmer and more nature - centered philosophy, Naruto could adopt some of that. He'd be less impulsive in his actions and more contemplative.