Well, Naruto is known for his strong sense of justice. In RWBY, this could be channeled in different ways. He might be more involved in the political side of things in the RWBY world, trying to bring about equality between humans and Faunus. His adoption could make him feel more responsible for the world he now calls home, and this would show in his more mature and thoughtful approach to problems, while still maintaining his core of being a fun - loving and energetic person.
His personality could also develop in new ways. Since the RWBY world has different social structures and challenges, Naruto could become more diplomatic. He'd have to interact with different races and factions, like the Faunus. So, he might learn to be more understanding and empathetic towards those with different backgrounds, which could add new layers to his already complex personality.
If adopted by Jiraiya, Naruto would probably be more self - assured. Jiraiya would instill in him a sense of pride in his abilities. He'd also be more of a free spirit. Jiraiya's influence would mean Naruto would be more likely to take risks and explore new things without as much hesitation as in the original story. He might also be a bit more flirty, as Jiraiya has his own charm when it comes to the opposite sex.
His personality might become more refined. Tsunade could teach him to be more patient and less impulsive.
Naruto's relationships would be different. He would have a father - figure in Jiraiya. Jiraiya could also introduce Naruto to new friends and allies. And Naruto would have more time to learn about his family and the secrets that Jiraiya might know about the Uzumaki clan. This could give Naruto a stronger sense of identity and purpose.
He'd probably be more reserved. Kakashi is not as boisterous as some others, so Naruto might pick up on that. For instance, he might not shout as much about becoming Hokage right away.
Naruto might become more reserved. Growing up under Zeltrech, he could be exposed to a more sophisticated and perhaps less rowdy environment compared to Konoha. So instead of his usual loud and brash self, he could develop a more calm and calculated side.
His personality would likely become more erratic. The Joker's influence is all about chaos and anarchy. Harry might start to laugh at inappropriate times and find pleasure in causing trouble just like the Joker. He could lose his sense of empathy as he is constantly exposed to the Joker's cruel and inhumane behavior.
Percy's personality could become more adaptable. The Avengers operate in a different world compared to where Percy is from. He'd have to learn new ways of doing things. So, he might become more flexible in his thinking and actions. Also, he could become more serious in some ways, as the Avengers often deal with high - stakes situations.
His personality might become more traditional in some ways. Since the founders are from an earlier time, their values could rub off on him. He might be more reserved like some of the older wizards.
His life would change drastically. He'd be surrounded by magic instead of ninjutsu. He might go to Hogwarts and have to study subjects like Transfiguration and Defence Against the Dark Arts. His daily routine would be completely different, from waking up in a dormitory to having meals in the Great Hall. He'd also have to follow the wizarding laws, which are very different from the laws in the ninja villages.
If Naruto gets adopted in RWBY fanfiction, it could lead to some interesting team - ups. For example, he could be paired with Ruby. Ruby is all about speed and her scythe - wielding skills, and Naruto's agility and combat skills would complement that. They could create some amazing battle strategies together. Also, Naruto's backstory of being an outcast at first could make him bond with characters in RWBY who have faced similar situations.