It could also be due to a prophecy or some sort of spiritual guidance. In the Naruto universe, there are often prophecies that guide the characters' actions. A prophecy might suggest that changing his name would bring about some great change or power. For instance, if there was a prophecy that a new name would help him unlock a hidden power or unite different ninja clans under a new banner.
Perhaps he would change to Naruto Storm. 'Storm' can represent his powerful and sometimes tempestuous nature. In the series, Naruto has shown great strength and determination that could be likened to a storm, which is both destructive and at the same time a force of change.
Perhaps he is trying to distance himself from his past self. Naruto has had a tough childhood and has been through a lot. Changing his appearance could be a way for him to start anew, to shed the image of the 'troublemaker' or the 'lonely kid'. He might want to present a new, more confident and respected image to the people around him, both friends and foes.
One common reason is love. If Naruto falls in love in a fanfiction, he may become more gentle and considerate, changing his usually rambunctious attitude. His focus could shift from just being the best ninja to also taking care of the person he loves.
It could be due to a new identity he wants to create for himself in a different magical community. Rial might be a name that is more acceptable or respected in that particular community. He may have fallen in love with the culture or values associated with that name and decided to make it his own.
Another reason could be a personal journey of self - discovery. Naruto might feel that his identity as the hero of the village has become a burden or a limiting factor in his growth. Changing his identity could allow him to explore new aspects of himself, away from the expectations and responsibilities that come with being Naruto Uzumaki.
Well, Naruto's personality could become more empathetic. In the male form, he was often brash and focused on his own goals. But as a girl, she might start to see things from other people's perspectives more easily. Maybe she'll be more in tune with the emotional needs of her friends and comrades, and this could change the dynamics of her relationships. Also, she might become more nurturing, which is a trait often associated with female characters in the Naruto universe.
Perhaps in the fanfic, Naruto is trying to fit into a different group or culture. His original hair style might make him stand out in a negative way in that context, so he changes it to be more accepted. Or it could be part of a bet or a challenge. For instance, he loses a bet with his friends and as a consequence, he has to change his hair style.
Naruto's relationships with his mentors could also change. They might start to treat him more as an equal, sharing more advanced knowledge with him. His relationship with Iruka sensei could shift from a teacher - student dynamic to more of a friendship between two equals. And with Kakashi, they could engage in more in - depth discussions about the ninja world and its future, as Naruto is now seen as someone who can contribute valuable ideas, not just a brash young ninja.
His character would become more secretive. Instead of being the open - hearted Naruto we know, he'd have to keep things to himself. For instance, he couldn't share all his thoughts and experiences with his friends right away.
Maybe a plot where Naruto's change in gender affects his relationships. His friends like Sasuke and Sakura might react in different ways. Sasuke could be more protective, or Sakura might see her as a new kind of rival or friend. Also, Naruto's relationship with his mentor Kakashi could change as Kakashi has to adapt to training a female ninja with Naruto's unique abilities.