Naruto's view of the world would expand. Meeting an entirely different kind of threat from another universe would make him realize that there are threats far greater than the ones he has faced in his own world. This could lead to him becoming more open - minded and willing to learn new skills and techniques from other sources. He might also become more empathetic towards other species, as he sees the destruction the Daleks can cause.
He could develop a greater sense of strategy. Daleks are technological foes, and Naruto would need to come up with plans that can counter their advanced weaponry. So he might study more about his enemies, like their weaknesses and how they operate. He could also become more of a diplomat, trying to find peaceful solutions first, as the Daleks are a force that could cause massive destruction in his world.
Naruto might become more cautious. Dealing with the Daleks, who are extremely dangerous and unpredictable, would force him to think before acting. His normal brashness might be toned down a bit.
Naruto might become more serious. Deadshot is a very serious and focused character. So Naruto could lose some of his goofy and carefree nature and become more calculating in his actions.
Naruto's character would likely become more calm and introspective. He'd focus more on inner peace rather than external battles.
Naruto's character would likely become more stoic. Vergil is known for his calm and collected demeanor, so Naruto might start to suppress his more exuberant emotions. He could become more calculating in battles, thinking several steps ahead like Vergil does when facing his enemies.
Naruto's character would likely become more withdrawn at first. The sudden change to being a frost demon would make him feel different from his friends. But as he learns to control his new powers, he'd become more confident. His sense of justice would still be there, but it might be tempered with the knowledge of his new, potentially dangerous abilities.
Naruto's character would take a dark turn. He might become more cynical. Instead of his usual optimistic self, he would view the world with suspicion. His sense of justice would be warped. He could start to believe that power is the only thing that matters, not the bonds he once held dear. His sense of humor might disappear as well, replaced with a cold and menacing demeanor.
He might become more stoic. Given the nature of Shinigamis, Naruto could grow up with a sense of calmness and detachment that's not typical in the original Naruto.
Naruto's character would likely become more confident. With a family structure provided by Mikoto, he would feel more secure. He might also become more mature as he is exposed to the Uchiha way of life. For example, he could learn discipline and patience more quickly. His understanding of the ninja world would expand as he learns from Mikoto about different clans and their relationships.
His view of the world would expand. Naruto, who was mainly focused on the ninja world, would now be exposed to the magical world through Merlin. This would make him more open - minded and understanding of different cultures and powers. He may also start to use his newfound knowledge to try and bring peace not just between ninja villages, but also between the ninja world and the magical realm Merlin comes from.
Naruto might become more sensitive and perceptive. Since kunoichi often have a different way of looking at things compared to male ninjas, Naruto could pick up on those traits.
Naruto's character would likely become more withdrawn. He's used to having people around him, but now, with everyone against him, he'd be more guarded. For example, he might not be as quick to trust new people.