His personality would likely become more conflicted. He has a good heart, but being around Bellatrix would make him question a lot of things. He might become more withdrawn as he tries to hide his true self from Bellatrix.
Well, Harry Potter's personality would be a mess. Bellatrix is a character full of hate and fanaticism. Harry would be under a lot of pressure. He might become more secretive, not wanting Bellatrix to know his true thoughts. His sense of right and wrong could be blurred as he's surrounded by Bellatrix's warped view of the world. But deep down, his inherent goodness might still be there, fighting against the negative influence, and this internal battle could make his personality complex and unpredictable.
His life would change drastically. He'd be surrounded by Death Eaters and the dark side of magic. His values would be challenged, and he might not have the same friends. He could become more feared in the wizarding world.
His personality would likely become more self - assured. Growing up with the founders, he'd be constantly exposed to great magic and wisdom, which would boost his confidence. He might also be more independent as he'd be trained in a more solitary way by the founders.
He might become more stoic. Gibbs' influence could make Harry hold his emotions in check more. Instead of being so impulsive sometimes, he'd think before acting.
If adopted by the Malfoys, Harry's personality would be a complex mix. He would be exposed to the Malfoy's elitist views from a young age. This could make him initially seem cold and distant. However, his innate goodness would still be there. He might struggle to reconcile his true self with the Malfoy persona he's expected to have. For example, he might be polite and proper in public as a Malfoy, but secretly help those who are oppressed by the pure - blood ideology, showing that his original kind - hearted personality is still fighting to surface.
His personality might become more confident, even a bit arrogant. Growing up in a rich family, he would be used to getting what he wants. For example, he might not be as humble as he was in the original story.
His personality would likely become more erratic. The Joker's influence is all about chaos and anarchy. Harry might start to laugh at inappropriate times and find pleasure in causing trouble just like the Joker. He could lose his sense of empathy as he is constantly exposed to the Joker's cruel and inhumane behavior.
His personality might become more traditional in some ways. Since the founders are from an earlier time, their values could rub off on him. He might be more reserved like some of the older wizards.
Naruto's chakra control could be seen as a form of wandless magic in the Harry Potter universe. His ability to create shadow clones might be adapted to create illusions that are more like the wizarding world's magic. For example, instead of a physical clone, it could be a magical apparition - like clone.
His life would be full of danger. Bellatrix is a volatile and dangerous person. Harry would be constantly surrounded by dark magic and the threat of Voldemort. He might not get the same kind of moral guidance he got at Hogwarts. His identity as 'The Boy Who Lived' would also be in jeopardy as Bellatrix might try to manipulate that for her own or Voldemort's gain.
The story would be drastically different. Harry might not oppose Voldemort. He'd be on the 'dark side' instead. His Hogwarts experience would be non - existent or very different if he even went there. He'd probably use the dark arts more often.