His relationships with others could change. If he's in a new dimension for a long time, he may form new bonds with characters there. These new relationships could influence how he views his old friends back in his original dimension. He might also learn new ways of communicating and building trust, which he can then bring back with him if he ever returns.
Naruto could meet alternate versions of his friends or enemies. For example, he might find a version of Sasuke who has a completely different personality or a different set of skills. This would create interesting interactions and potential conflicts or alliances.
Naruto's character would likely develop in many ways. In the new world, he might face new challenges that test his beliefs. For example, if the new world has different ideas about power and justice, he would have to reevaluate his own views. He may also become more self - reliant as he doesn't have his usual friends and support system right away. His experiences in this new world could make him more empathetic towards different races and species, as he discovers new ways of living and interacting.
Naruto's character could become more adaptable. Facing the unknown in the parallel dimension, he has to quickly adjust to new situations, which would make him more flexible in his thinking.
In dimension travel fanfictions, Naruto usually gains a broader perspective. When he sees different versions of his friends or different ninja cultures in other dimensions, he starts to question his own beliefs and values. This leads to his growth as he becomes more open - minded and understanding. He may also face new challenges that test his courage and determination in ways he hasn't experienced in his own dimension, which further hones his character.
He would probably become more mature faster. Being in the past, he would face different challenges compared to his own time. This could force him to think and act more strategically, thus enhancing his growth as a ninja and as a person.
Naruto's character would likely develop a stronger sense of family loyalty. Growing up in the Uchiha clan under Fugaku's care, he'd be immersed in a culture that highly values family. He might also become more secretive, as the Uchiha often keep their cards close to their chest. This would be a big change from the open - book Naruto we know. Additionally, he could gain a more nuanced understanding of power, since the Uchiha are known for their powerful Sharingan and thirst for strength.
Naruto's character would develop in a very different direction. He'd likely be more stoic and less impulsive. Since Kaguya has a more detached view of the world, Naruto might inherit some of that. He would be more calculating in battles, using his powers in a more precise way rather than relying on his usual head - on approach. His sense of justice might also be warped as he grows up under Kaguya's teachings, which are different from the values he was taught in the original story.
His character could become more complex. He'd have to balance his own values from Konoha with the new ones in the Covenant. This internal struggle would likely make him more mature. For example, he might question his previous beliefs about power and leadership.
His character might become more refined. Growing up in a Daimyo's family would expose him to different values and cultures. He could become more diplomatic and less brash.
Naruto would likely become more in tune with nature. The Inuzuka's connection to their ninja dogs and the outdoors would influence him. He might be more reserved at first as the Inuzuka have a different family dynamic compared to what he's used to. But as he grows, he would become more confident in his abilities within the clan's framework.