His temper might be more volatile. The Kyuubi's influence could make him quicker to anger, especially when someone threatens his friends or the village. However, he also has better control over his emotions in other cases as he has to manage the power of the Kyuubi. He can't let his emotions run wild all the time. He might be more withdrawn in some aspects, spending time to understand and control the new power within him, rather than being as outgoing as he was before.
Naruto may develop a more serious side to his personality. Since having the full Kyuubi is a huge responsibility, he might feel the need to act more maturely. He starts to think more strategically in battles and in his interactions with others. He also might become more empathetic towards the Kyuubi, seeing it not just as a source of power but as a being with its own history and feelings, which in turn affects his overall personality.
He becomes more nurturing. Naruto, who has always had a big heart, now channels that into taking care of his daughter. He listens to her more intently, tries to understand her feelings, and is always there to offer support and advice, just like a good father should. He might also be more patient than he used to be. For example, if his daughter is having trouble learning a new ninjutsu technique, instead of getting frustrated like he might have in the past, he'll patiently guide her through it step by step.
Naruto's usually positive and determined personality could become more aggressive. He might lose his sense of humor and be more focused on power and destruction in his demon form.
His confidence could increase significantly. Being turned into a kitsune, a creature often associated with wisdom and power in the Naruto universe, Naruto might feel more self - assured. He may become more decisive in his actions, knowing that he has these new powers and a different form.
He may become more aggressive. The power of the nine - tails can influence his normal calm and determined self, making him more likely to act on impulse and attack first without thinking too much about the consequences.
Naruto's personality might show a more serious side. Wearing a suit could make him feel more responsible, like he has to represent the Hidden Leaf in a proper way. So he'd be less likely to crack jokes and more focused on the task at hand.
Naruto might become more calculating. Since Mewtwo is very intelligent and has powerful psychic abilities, Naruto would have to use his mind more. He would think before acting, unlike his impulsive self in the original series. This change could make him a better strategist in battles, but it could also lead to misunderstandings with his friends who are used to his more straightforward and impulsive nature.
Naruto's personality could shift towards being more reserved. As a Shinigami, he has to deal with the weight of handling souls and the concept of death. This could make him think twice before acting impulsively like he used to. He may also develop a more empathetic side towards those who are about to die or have lost loved ones, as he now has a closer connection to the afterlife.
His combat abilities are enhanced greatly. With full control of the Kyuubi, Naruto can access its chakra more freely. This means he can enter the Nine - Tails Chakra Mode without the risk of losing control. His physical strength, speed, and endurance are boosted to superhuman levels. For example, he can move at incredible speeds, dodge attacks more easily, and deliver more powerful punches and kicks.
If Naruto becomes a Hunter Nin in fanfiction, his personality would change significantly. He'd be more calculating. His usual impulsive nature would have to be toned down because one wrong move as a Hunter Nin could mean disaster. He might also become more solitary, used to working alone in the shadows rather than in a team. His sense of humor might also be more subdued as he takes on this serious and dangerous role.
He would likely become more irreverent. Naruto is usually quite earnest and determined, but as Deadpool, he'd be cracking jokes all the time, even in serious situations. With Fem Kyuubi around, he might tease her constantly. For example, he could make fun of her tails or her sometimes - haughty attitude. His sense of morality might also shift a bit, becoming more in line with Deadpool's grey - area ethics.