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.
He might be more arrogant. Growing up with the Malfoys, he'd be used to thinking his family was superior. He'd lack the humility Harry in the original series has.
His personality could become more reserved. Growing up in the Malfoy household, he might be taught to keep his emotions in check and not show too much vulnerability. But at the same time, his underlying sense of right and wrong would still be there, causing internal conflict.
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 He might become more withdrawn as he tries to hide his true self from Bellatrix.
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.
His personality would likely be a blend of his natural Gryffindor traits and the influence of the Malfoy family. He might become more guarded and calculating at times, due to the Malfoy's sly nature. But his underlying sense of justice and loyalty would still shine through. For example, he might be more hesitant to trust people initially compared to in the original story.
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.
He might become more refined in his manners. The Malfoys are a very proper pure - blood family, so Harry would likely be taught to act more like them. For example, he'd probably have better table manners and a more sophisticated way of speaking.
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.