Naruto would probably be more cerebral. Since Robin is known for her intelligence and love for knowledge, Naruto might spend more time studying and analyzing situations rather than just jumping into action. He could be more strategic in his battles, thinking several steps ahead like Robin often does.
He would likely have a different sense of family and belonging. Robin has her own backstory and relationships, and Naruto being her son would mean he has a different set of family dynamics. This could make him more introspective about his place in the world and more cautious about who he trusts. He might also be more empathetic towards those who are outsiders or have a difficult past, as Robin herself has been through a lot.
Naruto would likely be more conflicted. His usually bright and positive personality might be tempered by the knowledge of his dark heritage. He might become more cautious in using his power, knowing the destruction Thanos was capable of. He could also be more isolated as other characters might fear his potential for evil.
Naruto's sense of humor would definitely change. He would likely have a much darker and more sarcastic sense of humor, like Deadpool. His confidence might also skyrocket in a different way. Instead of just believing in himself as a ninja, he'd believe in his ability to break all the rules like Deadpool does. He might also be more open to using unethical means to achieve his goals, which would be a big shift from his normal self.
He would likely be more brooding. Naruto is usually a very upbeat character, but if he was the son of Dracula, he'd have to deal with the dark side of his nature. He might be more withdrawn, especially if he was worried about hurting others with his vampire powers.
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.
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 He has to learn to control these new powers, which might make him seem more withdrawn as he trains in isolation to avoid hurting others accidentally.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.
He might become more cynical. Growing up with Cersei as his mother, he would be exposed to a lot of political backstabbing and power - mongering. But his original Naruto - like optimism might still peek through at times. For example, he could initially be distrustful of people but then find a few he truly believes in and regain some of his more positive outlooks.