Naruto's character would change in several ways. His sense of loyalty would be tested. As a vampire, he might be more tempted to put his own needs (like finding blood) first. Emotionally, he could become more brooding. He's used to being the energetic one, but now he has to hide his vampiric nature. This could lead to him distancing himself from his friends. Also, his ninja skills would take on a different aspect. His stealth might improve because he has to move in the shadows more, but his use of some jutsu that require sunlight or open areas could be compromised.
Naruto would become more brooding. His usual cheerful self would be dampened by the dark nature of being a vampire slave. He'd be more secretive as he has to hide his new condition from his friends at first.
His character would have a darker edge. The vampire nature could bring out a more primal and possessive side. And the Rinnegan would give him new levels of power and knowledge. He might start to question his old values as he realizes the potential of his new powers. He could become more solitary, training alone to master his combined abilities rather than relying on his friends like he used to.
Naruto would become more brooding. His usual sunny disposition would be tempered by the knowledge of his vampire side. He'd be more cautious about his relationships, fearing he might accidentally harm his friends. For example, he might be hesitant to get too close physically during hugs or high - fives in case his vampire strength gets out of control.
Naruto's character would likely become more sensitive. As a girl, she might be more in tune with her emotions and those of others. She may also become more cautious in some ways, as she'd have to deal with different threats and challenges related to being female in the ninja world.
His relationship with Tails would be strained. Tails would be confused and a bit scared at first. Sonic would have to hide his new vampiric urges from Tails, which would create distance between them. With Knuckles, there might be more of a distrust as Knuckles is very protective of their world. Knuckles might see Sonic as a threat now that he's a vampire.
He might become more logical. Since robots are often programmed with certain algorithms, Naruto could start to think more in terms of cause and effect rather than just his usual impulsive ninja instincts.
He might become more brooding. The new powers and the vampiric nature could make him a bit more withdrawn as he tries to understand and control his abilities. But his core of kindness would still be there.
His relationship with his sensei, Kakashi, would change significantly. Kakashi would be more cautious around Naruto, not fully understanding the implications of his new vampire state. At the same time, he would try to guide Naruto in controlling his new powers. Naruto would look to Kakashi for help but also feel a sense of isolation as he realizes he's different from the other ninjas. And his friendships with the other Konoha 11 would be strained. They might be afraid of him, or he might push them away to protect them.
Naruto's life would be completely different. He'd be part of a vampire family, which means different social norms and rules. He might not be able to be as open with his old friends as before. And he'd have to learn about vampire history and lore, which could be both fascinating and terrifying. His identity as a ninja would be in conflict with his new vampire identity in some ways, like when it comes to using violence. Vampires have their own way of dealing with threats that might not align with the ninja way.
For Naruto, his normally energetic and positive nature might be clouded by the darker aspects of being a vampire. He might struggle with the urge to drink blood, which could make him more withdrawn at times. However, his determination to protect the village and his friends would still be strong.