Well, Naruto's personality might change in a few ways. He could become more self - reliant. Without his family to rely on, he has to fend for himself. So he'll learn to do things on his own, like find food and shelter. He might also become more cynical. If his family situation was bad enough to make him run away, he may start to view the world in a darker light. He could start to believe that people are generally not to be trusted. But at the same time, he could also become more empathetic. Knowing what it's like to be in a difficult family situation, he may be more understanding of others who are in similar situations.
He could become more withdrawn. Since he's running away from family, he may lose some of his usual outgoing nature. For example, he might stop being as eager to make friends or be part of a team. He may also become more distrustful. After leaving his family, he might start to question the motives of others more, suspecting that people are like his family in some way.
Maybe he feels misunderstood by his family. In many Naruto stories, his family situation can be complex. If he's 'godlike', he might have powers that his family doesn't understand or fears, leading him to run away to avoid conflict or being treated differently.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
Perhaps Naruto feels that Kushina is being overprotective. He wants to prove his independence and go on his own adventures without her constant supervision, so he decides to run away.
One possible reason could be that Naruto might be afraid of the intense training Jiraiya has in store for him. Jiraiya is known for his strict and grueling training methods, and Naruto, being young and sometimes impatient, might just want to escape that for a while.
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.
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.