There could be other young witches or wizards who are also on the run from something or have their own issues with the wizarding establishment. They bond with Harry over their shared experiences and together they face new challenges. Maybe a young witch who has unique powers related to nature and she helps Harry understand the more elemental aspects of magic.
Sometimes, a magical creature befriends Harry when he leaves the Dursleys. It could be a phoenix - like creature that has the ability to heal and guide. This creature becomes Harry's constant companion and provides him with both emotional support and magical assistance in his new adventures.
Dudley can also be a fascinating character to write about. You could show his growth from a bully to someone who might start to understand Harry. Maybe he has a secret admiration for Harry's magical abilities.
Petunia Dursley is also quite popular. There are fanfictions that delve into her past, her relationship with Lily, and how that affects her treatment of Harry. Some stories might show her having a change of heart and trying to make amends with Harry in a more complex way than just the basic storyline in the original books.
Obviously, Harry Potter himself is the most important character. He is the central figure around whom the whole story of abuse and his journey to overcome it revolves.
Often, there are new vampire characters. Maybe a vampire who was once a famous historical figure, like a medieval knight turned vampire. There could also be a witch - vampire hybrid who becomes Bella's friend or foe. Another common addition is a vampire with a special power related to the mind, who tries to influence Bella after her transformation.
Often, there are midwives or healers that are introduced. These could be ancient vampires with special knowledge of hybrid births. Another common new character is a seer or prophet who can predict the future of Bella's baby. Sometimes, there are also new werewolves who come to protect Bella during the birth because they sense a great change is coming.
Voldemort or his followers could also be relevant in some stories. Maybe Harry is leaving because he fears a resurgence of Voldemort's forces and wants to find a way to defeat them from afar. Or perhaps some of Voldemort's old followers are still after him, and his leaving is a way to draw them away from the innocent people in Britain.
Some fanfictions introduce a new transfer student from a far - flung wizarding school. This character often brings in new magical knowledge and different cultural perspectives. Another interesting new character could be a young teacher who has a really unique teaching style. For example, a teacher who specializes in teaching forgotten or ancient magics that the students are eager to learn.
Definitely Dudley. In fanfic, he can be developed in so many different ways. He could become a wizard himself, or he could befriend Harry in a more meaningful way than in the original books. Another interesting character is Petunia. There could be more exploration of her past and her relationship with Lily, which can make her character more complex.
In this fanfiction, perhaps a new character is an old wizard who has been trapped inside the mirror for centuries. He has a lot of ancient magic knowledge and he becomes a mentor - like figure to Harry. He helps Harry understand the true power of the mirror and how it can be used to save the wizarding world from a new threat.
Obviously, Harry Potter is a main character as the story is centered around him as a baby at the Dursleys. Then there are the Dursleys themselves - Vernon, Petunia, and Dudley. Vernon is the strict and often cruel uncle, Petunia is the conflicted aunt who has her own issues related to the wizarding world, and Dudley is the spoiled cousin.