Naruto could be more empathetic towards the Uchiha's cause. Since Mikoto is his mother figure, he would be exposed to the Uchiha's history and their grievances from a young age. This would make him more understanding of Sasuke's later actions and more likely to try and find a peaceful solution for the Uchiha's problems.
He might be more aloof. Since a phoenix is a rather otherworldly creature, Naruto could pick up some of its more detached qualities. He may not be as quick to make friends as in the original story, instead observing more from a distance before approaching others.
His personality would likely be more reserved and calculating. Since Danzo was a very secretive and shrewd character, Naruto might inherit some of those traits. He may not be as open and trusting as in the original series.
His personality might be more serious. Since Onoki is a no - nonsense leader, Naruto could pick up that trait. He might be less impulsive and more calculating in battles.
Naruto might be more distrustful. Since Kabuto has been involved in many underhanded schemes, Naruto could grow up thinking that everyone has ulterior motives. This would be a big change from the original Naruto who was so quick to trust and befriend others. He would also probably be more self - reliant as Kabuto may not encourage the same kind of teamwork that Naruto was exposed to in Konoha. He would be more likely to rely on his own skills and knowledge, which could make him a more solitary figure in the ninja world.
Naruto might be more distrustful of the Hidden Leaf Village. Since he's being raised by a missing - nin, he would hear different perspectives that might make him question the village's motives and actions.
One interesting type is where Naruto has a more introverted personality. Instead of being the boisterous and outgoing Naruto we know, he's quiet and more of an observer. This changes his interactions with his friends, like Sasuke, who might initially be more confused by this new Naruto. Another could be a Naruto with a super serious personality, focused solely on becoming Hokage in a very strict and no - nonsense way, losing some of his child - like charm but gaining a different kind of respect from the villagers.