His life would become much more exciting. Naruto would have a new creature to take care of, which is a big change from his normal ninja life. He'd need to learn about dragon care, which could lead him to new places and new knowledge. And he'd have a powerful friend once the egg hatches.
If Naruto found a devil fruit, it would open up a whole new world of possibilities for his adventures. He could travel to different lands in search of more knowledge about the devil fruit. Maybe he'd encounter other characters from different fictional universes who are also interested in devil fruits. His understanding of power and the world around him would expand. He'd no longer be just a ninja from the Hidden Leaf, but someone with a power that bridges different fictional concepts. This could lead to him becoming a sort of ambassador between the Naruto world and the world of One Piece - like elements introduced by the devil fruit.
Naruto's character could change in several ways. Firstly, he might become more secretive as he tries to figure out what the gun is without causing panic. He's always been an open book, but this strange discovery might make him hold back some information. Secondly, he could become a bit more of a loner as he delves into understanding the gun on his own. He might feel that his friends won't understand this new aspect of his world. Also, his sense of right and wrong could be challenged. The gun's lethality is different from his normal weapons, and he'd have to decide how and when it's appropriate to use it, if at all, which would be a big shift in his character.
His relationship with his sensei, like Kakashi, would also change. Kakashi would have to train Naruto to control his dragon powers. Naruto might be a bit more rebellious as a dragon, feeling the freedom that comes with his new form. But Kakashi would still be there to guide him, and their bond would transform into one that focuses on Naruto's new abilities and how to use them for the good of the village.
His living situation would be different. He'd live in the Hyuga compound, which is a very traditional and family - centered place. He'd probably have a proper family structure for the first time. And he'd be surrounded by people who are highly skilled in combat and chakra control.
If Naruto was adopted by Rias in fanfiction, his life would take a completely new direction. He would be in a world full of magic and supernatural beings. His daily routine would change from ninja training to learning about devil magic and the ways of Rias's peerage. His relationships would shift too. He might form strong bonds with the members of Rias's group, sharing his own stories of growing up as an outcast in the ninja world. His combat style would also evolve as he incorporated elements of devil magic into his ninja techniques. And his presence could potentially change the power dynamics within Rias's peerage, bringing new strategies and ideas to their battles and operations.
His life would become more domestic. He would have to worry about things like feeding the cat and cleaning its litter box. Also, he would have a constant companion at home, which would make his place feel more like a home rather than just a place to sleep.
If Naruto is adopted by the Kazekage in fanfiction, his training would be different. The Kazekage would likely teach him unique Suna - style jutsu. His growth as a shinobi would be shaped by Suna's traditions. Also, his identity would be more tied to Suna. He'd be seen as a part of Suna's future, and this would affect how he views himself and his place in the ninja world.
If Naruto was born in Ame in fanfiction, his relationships would be vastly different. He wouldn't have the same bond with characters like Iruka or Kakashi. Instead, he'd form connections with people in Ame, who might be more focused on survival and power - grabbing. His enemies would also be different, perhaps facing more internal power struggles within Ame rather than the external threats that Konoha usually deals with.
Naruto's life would be completely different. Tsume is a strict and proud character. Under her care, Naruto would likely be pushed to his limits in training. He would also have a different living situation. Instead of living alone in his small apartment, he'd be in the Inuzuka compound. He might be given a ninja dog of his own early on, which would change his combat style and how he approaches missions.
His living situation would be much different. Instead of living alone, he would be part of a large clan. He'd have a proper family structure with elders, siblings perhaps, and aunts and uncles. This would give him a sense of belonging that he lacked before.