If Hermione was raised by Voldemort in fanfiction, she might have a completely different personality. She could be more ruthless and power - hungry. Her magic might be used for more dark purposes. For example, she could be trained to be one of Voldemort's most powerful lieutenants, using her intelligence to plan his attacks and strategies.
In a fanfiction where Hermione is raised by Voldemort, it would be a very dark and complex story. She would probably be isolated from the normal wizarding community that she once belonged to. Her friendships with Harry and Ron would never have developed in the traditional way. Instead, she might be pitted against them. Voldemort would surely use her intelligence to try and gain an upper hand in his fight against those who oppose him. But Hermione might also retain some of her own sense of justice deep down, which could lead to a possible redemption arc or a major internal struggle throughout the story.
In such a fanfiction, Harry might become a very different person. He could be more in tune with the Dark Arts. Maybe he would have a skewed sense of morality, influenced by Voldemort's views. He might also be more powerful in the Dark Arts but struggle with his identity as he is constantly in conflict between what he's been taught by Voldemort and his own inner goodness.
If Hermione was Voldemort's daughter in fanfiction, she might struggle with her identity. She's always been on the side of good, but this new knowledge could make her question everything. Maybe she'd try to hide it from her friends at first.
If Hermione was raised by Bellatrix in a fanfiction, it would be a very dark and twisted story. Bellatrix is a cruel and insane character. Hermione could be forced to participate in dark deeds. But on the other hand, Hermione's intelligence might make her find a way to resist Bellatrix's influence secretly. She could use the knowledge of the dark magic she gains to better understand how to fight against it in the long run.
She might face a lot of internal conflict. On one hand, she has been raised with the values of Gryffindor, like courage and justice. But on the other hand, she has this dark heritage. This could lead to a really interesting character arc where she has to constantly battle her inner demons. For example, she might be tempted by the power that her relation to Voldemort could potentially bring, but she has to resist it to stay true to herself.
In this fanfiction concept, Hermione would be facing a terrifying situation. Given to Fenrir by Voldemort, she'd be in a world of trouble. Fenrir's werewolf nature would make him unpredictable and dangerous. But Hermione has her wits about her. She could attempt to communicate with Fenrir, perhaps trying to appeal to any sense of humanity he might have left, though it's likely to be a long shot. She might also try to use her connection to Harry and Ron, hoping they would come to her rescue. And if she has access to her wand, she could perform spells to protect herself, like a Patronus charm to keep Fenrir at bay, at least temporarily.
She would likely be more guarded and distrustful. Growing up with Voldemort, she would have seen a lot of dark and cruel things. So, she might not be as open and friendly as in the original story. For example, she might not be so quick to trust Harry and Ron when she first meets them.
In such a fanfic, it would be a very strange and dark twist. Voldemort might use Harry and Hermione to gain more power in a different way. Maybe he wants to corrupt them and turn them against Dumbledore and the Order. He could also try to use their knowledge, especially Hermione's vast magical knowledge, for his own evil plans.
Her Hogwarts experience would be extremely different. She might enter Hogwarts as a sort of spy for Voldemort. Instead of being sorted into Gryffindor, Voldemort could have influenced the Sorting Hat to put her in Slytherin. She would be looked at with suspicion by most of the teachers and students who knew of her connection to Voldemort.
Maybe she discovers a hidden prophecy that states she has the power to either destroy Voldemort or become his most powerful ally. This would create a great internal struggle for her as she was raised by him but also has a sense of good. She might start to manipulate Voldemort into making decisions that would eventually lead to his downfall.
In such a fanfiction, Harry might be raised with a very different set of values. Voldemort could try to mold Harry into his own image, perhaps teaching him dark magic. But Harry might also secretly hold on to his own sense of good. For example, he could use the knowledge Voldemort gives him to ultimately turn against him.