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'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 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.
His character might be more hardened. Growing up with Yahiko, he'd be exposed to the harsher side of the ninja world earlier. So he'd be less likely to trust blindly.
Naruto's character would likely become more calculating. He'd still have his core values of friendship and protecting his village, but he'd approach things with more cunning. For example, in battles, he might study his opponents' weaknesses more carefully before attacking. His social skills could also change. He might be more selective about who he trusts, using his Slytherin side to analyze people's motives.
Naruto's character would likely become more reserved at first. Konan's calm and collected nature might rub off on him. But he'd still keep his core of determination. He'd probably learn to be more strategic in combat, taking after Konan's planning skills. His view on the world might also change as he grows up in the Hidden Rain Village instead of Konoha.
In a fanfiction where Naruto is in the Akatsuki, his character would grow in terms of understanding different perspectives. He'd interact with characters who have very different backgrounds and motives from his friends in Konoha. His sense of loyalty would be tested as he'd be in a group that is generally considered the enemy. This could lead to him becoming more independent in his decision - making, rather than relying on the approval of his village. He might also become more calculating, as the Akatsuki often have to plan their moves carefully to avoid detection and achieve their goals.
In the fanfiction, the hawk summon might expose Naruto to a different side of the ninja world. This could make him more empathetic towards other creatures and shinobi who have unique summons. It could also make him more responsible as he has a new powerful ally to take care of.
Naruto would be more disciplined. Gai's strict training regime would make him more focused on his goals.
Naruto would likely be more confident. Since Hiruzen is a respected figure, Naruto would grow up feeling more secure. He'd probably be less impulsive as he'd have Hiruzen's wisdom to guide him.