He might be more diplomatic. Growing up as the son of a queen would expose him to a lot of political situations. So, instead of just rushing into fights, he'd try to resolve conflicts through negotiation first. However, his hot - blooded nature would still be there, and when pushed too far, he'd fight back with all his might. Also, he may have a sense of entitlement due to his royal blood, but at the same time, his experiences in the ninja world would keep him grounded and make him realize that everyone is equal in the face of danger.
Naruto would likely be more refined in his manners. Since he's the son of a queen, he'd probably grow up with a certain level of etiquette. But he'd still keep his core values of never giving up and protecting his friends.
Naruto's normally bright and positive personality might become more conflicted. Since Douma has a more complex and often morally ambiguous nature, Naruto would have to grapple with new emotions. He might become more reserved as he tries to figure out how to handle Douma's powers without losing his own identity.
Naruto could also become more powerful but in a different way. His chakra might be tainted with a touch of the demonic, giving him new abilities that are both a blessing and a curse. He has to learn to control these new powers, which might make him seem more withdrawn as he trains in isolation to avoid hurting others accidentally.
He might become more devious. Instead of his straightforward, head - on approach, he could start using more underhanded tactics, like Loki. For example, he may set up elaborate traps for his enemies rather than just fighting them directly.
Naruto could become more empathetic. Since Hestia is often associated with warmth and care, he may inherit some of those traits. So, instead of just being the loud and brash Naruto we know, he might be more in tune with the feelings of others, especially those who are suffering or in need. This could change the way he forms relationships in the Naruto world, and he might be more likely to offer a helping hand even to his enemies under certain circumstances.
He would likely become more in tune with nature. Since Artemis is associated with nature and the hunt, Naruto might have a deeper respect for the natural world. He could be more stealthy, like a hunter, and his combat style might incorporate more fluid and quick movements similar to how one would move while hunting. Also, his values might shift a bit, with a stronger emphasis on protecting the natural balance.
He might become more carefree. Dionysus is often associated with merriment, so Naruto could be less burdened by his usual troubles. For example, he might joke around more during serious missions.
His relationship with Sasuke would likely become more complex. Sasuke might initially feel pity for Naruto, but then respect him more as he sees Naruto still being strong despite his blindness. He could become more protective of Naruto, which is a big change from their usual competitive relationship. With Sakura, she would probably be more motherly towards Naruto, constantly worried about his well - being and trying to find medical jutsu to cure his blindness.
Naruto might become a bit more reserved. Since Ulquiorra is a rather cold and stoic character, Naruto could start to hold back his more exuberant emotions. He might also become more analytical, like Ulquiorra, when it comes to combat situations. Instead of charging in head - first all the time, he'd think more about the best approach.
He might become more brooding and serious. The connection to Hades could bring out a darker side to his personality.
He might become more confident, bordering on over - confident like Gilgamesh. Naruto is already confident, but with Gilgamesh as his father, he could have an even greater sense of self - importance.