Naruto's character would change in several ways. Firstly, his sense of justice might be warped. He might not fight for the right reasons like protecting his friends and the village, but rather just to complete missions as a weapon. His optimism would likely disappear as he'd be constantly in a state of being used. His relationships would also be different. He may not have the close - knit group of friends as he does in the original series. Instead, people might be more like his handlers or superiors. His dreams would no longer be about becoming Hokage to gain recognition and bring change, but perhaps just about surviving as a weapon.
He would be more cold - blooded. Instead of the warm - hearted Naruto we know, he'd be focused on combat and following orders. His personality would lack the playfulness and the drive to make friends.
Naruto's character would become more in tune with Arachne's characteristics. He could be more patient and calculating. Since Arachne is often associated with webs and traps, Naruto might be more strategic in his battles and less impulsive. He may also have a different sense of loyalty, not being as blindly loyal to a village as he was in the original story.
He'd be more cynical. Jenova is a malevolent force, so Naruto would likely lose his optimistic outlook.
Naruto's personality would likely be more reserved. Instead of being the loud and boisterous Naruto we know, he might be quieter, observing from the shadows more often. Since foxes are often solitary animals, he might have a harder time making friends initially. But on the positive side, he'd be extremely adaptable, able to survive in tough conditions just like a fox in the wild.
He'd be more cynical. Orochimaru's ways would make Naruto question the goodness in people.
It could also change his stealth abilities. Since it's a shadow weapon, it may allow Naruto to blend into shadows more easily, making it easier for him to spy on enemies or launch surprise attacks. This would be a great advantage in his ninja missions.
If Naruto was raised by Vegeta, his character would likely become much more aggressive and focused on power. Vegeta's Saiyan pride and his constant drive to be the strongest would rub off on Naruto. He might not be as friendly or as empathetic as in the original series, but would instead be more solitary in his pursuit of strength, seeing it as the ultimate goal.
His character would likely become more grounded. Since the Earth Country has a more practical and stable culture, Naruto might not be as impulsive as he is in the original story. He would probably be more attuned to the physical aspects of being a ninja, like earth - based jutsu and building strong defenses.
His physical strength might increase. Dwarves are often depicted as strong, and living among them could mean Naruto has to do a lot of physically demanding tasks like mining or lifting heavy objects. So, he'd likely have more brute force.
If Naruto was raised by Orochimaru in fanfiction, his relationships would be turned upside down. His friendships from the Leaf Village would be in jeopardy. Since Orochimaru is not one to value the kind of loyalty and friendship that Naruto's friends in the Leaf do, Naruto would have a hard time understanding and maintaining those relationships. He might even be hostile towards them, seeing them as obstacles in his pursuit of power. His relationship with the Hokage would also be a mess. Instead of looking up to the Hokage as a role model, he would probably view the position as something to be conquered or undermined, following Orochimaru's ideology of power - seeking.
His abilities would likely become more brutal. The Espada are known for their raw power and direct combat styles. Naruto might not develop his signature jutsu like the Rasengan in the same way. Instead, he could focus more on melee combat and dark - based energy attacks similar to what the Espada use.