He could be portrayed through his appearance. For instance, one personality might have different - colored eyes or a distinct style of dressing. His behavior would also change. When in one personality, he could be very talkative and energetic, and when in the other, he could be silent and brooding.
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 He could be more withdrawn as he grapples with the strange and often terrifying aspects of Slenderman's world.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.
His personality would likely be more stoic. Kisame is a rather reserved and tough character, and growing up with him would probably make Naruto less exuberant. He might not be as quick to trust others as he is in the original story.
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 Instead of his usual sunny and determined self, he could be more withdrawn as a dark cleric, constantly thinking about the implications of his new powers and the dark path he's on.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.