He might change in terms of his magical abilities. Maybe the Malfoy family focuses on different types of magic than what Harry was exposed to in the original story. So, he could be more proficient in dark arts - adjacent magic, but also struggle with the moral implications of using such magic. He may have to reevaluate his own identity and what it means to be a 'good' wizard.
He becomes more conflicted. Growing up as Lucius Malfoy's son, he is exposed to different values. So, instead of the Gryffindor - like straightforwardness, he may have a more calculating side.
In 'Harry Potter son of Loki' fanfiction, Harry changes significantly. His sense of identity is greatly shaken. He no longer just sees himself as a simple wizard. He now has this connection to Norse mythology. This makes him more curious about different forms of magic and otherworldly things. He may become more of an outcast as well, since his heritage is so different. But this also makes him stronger in some ways. He has to rely on himself more and develop his own unique set of skills and powers that come from both his Potter and Loki lineage.
In this fanfiction, Harry's change is quite significant. Firstly, his view of himself and his place in the world is completely altered. Instead of just being a wizard, he is now part of something much bigger. This new identity gives him a different kind of courage. He's not just fighting for the wizarding world against Voldemort, but also has a connection to Asgard. His relationships with his friends also change. They might see him in a new light, and he might have to deal with their different reactions. He could become more of a leader, using his new powers and status to inspire others. And his magic might even be influenced by his Asgardian heritage, making it more powerful or having different manifestations.
Harry in this fanfiction might be a lot more complex. His identity is no longer that of the Boy Who Lived in the traditional sense. He has to come to terms with the fact that his parents are two very different and controversial figures. He may become more of an outcast, even among his friends at Hogwarts. His sense of right and wrong could be more blurred, as he has the influence of Bellatrix's dark ways and Snape's own morally ambiguous actions. He might be constantly questioning his own nature and whether he is destined to follow a path of good or evil.
His character becomes more independent. As the son of Artemis, he has a different kind of power and heritage that sets him apart from other wizards. This could lead to him relying less on the help of others and more on his own instincts and abilities. He might also be more secretive about his new powers, which adds a new layer of mystery to his character. For example, he could start to disappear at night to train in the moonlight without telling his friends.
He becomes more conflicted. Knowing he's Voldemort's son, he's constantly in turmoil about his true nature. His confidence might waver as he wonders if he's capable of the same evil as his father.
Well, if Harry was Lucius Malfoy's son, it would completely flip the story. Harry would be brought up in a pure - blood supremacist family. He might not have his kind heart as we know it. His relationship with Ron and Hermione would be non - existent or very different. He would probably be taught dark magic from a young age instead of the values he learned at Hogwarts in the original story.
He'd probably be more morally ambiguous. Growing up as Crowley's son, he might not have the same clear - cut sense of right and wrong as the original Harry. He could be more cunning and less hesitant to use underhanded tactics if necessary.
He might become more in tune with nature. Since the Phoenix is a symbol of rebirth and nature in the wizarding world, Harry could develop a stronger sense of environmental magic. For example, he could be able to communicate with other magical creatures more easily, not just the Phoenix.
Harry's character could change in that he becomes more of a leader. With the special abilities and heritage from Hecate, he may find himself in situations where he has to take charge. He might also develop a deeper sense of responsibility, not just for his friends but for the wizarding world as a whole. He realizes he has a different role to play now that he is the son of a goddess. Also, he could become more attuned to the more mysterious and darker aspects of magic, which might make him seem a bit more brooding at times.