She could be an ancient Celtic goddess, like Brigid. Brigid is associated with magic, healing, and smithcraft in Celtic mythology. In the fanfiction, she might see Harry's potential and decide to train him in her unique magical arts.
It could be a completely original goddess created just for this fanfiction. Maybe she is the goddess of a forgotten element, like the goddess of lightening that has been long forgotten in the ninja world, but still holds great power.
One possible goddess could be Athena. In the context of the fanfiction, she could bring her wisdom and strategic skills to help Harry Potter. Another could be Aphrodite, adding an element of love and charm to the story, perhaps using her powers to influence the emotions of characters for good or bad depending on the plot.
It could be an unknown character who has been in hiding all this time. Maybe she was once a powerful witch who made a pact with death and became its representative in the wizarding world.
One common theme is identity. Since Harry is adopted, he may struggle with who he really is in relation to his new family and his wizarding heritage. Another theme could be family dynamics, as he has to adapt to a new family structure. And there's often the theme of secrecy, as his adoption might be something that needs to be hidden for some reason in the wizarding world.
In this kind of fanfiction, Harry often becomes more proficient in potions and other areas that Snape is good at. His relationship with Snape also makes him more empathetic towards Snape's past and the Slytherin house in general. He may not be as quick to judge people based on their house. Also, he might develop a more complex view of the wizarding world's politics, as Snape is deeply involved in some of the darker aspects of it.
In this fanfiction, perhaps there would be a lot of magical adventures combined with the relationship between Harry Potter and the goddess. Maybe they would use their combined powers to face new threats to the wizarding world.
Well, if Harry Potter becomes a goddess in fanfiction, he could bring about a new era in the wizarding world. His new form might allow him to access magic that was previously unknown. He could start to teach other wizards and witches about this new magic, changing the way magic is practiced. Also, he might face challenges from the wizarding establishment who are afraid of his new - found power and the changes he could bring. But he would also have many supporters who believe in his good intentions and the positive changes he could make.
One possibility could be Morgana. In some interpretations, she has powerful magic and could be reimagined as a more benevolent Goddess of Magic in the Harry Potter universe. Another could be a completely new character created specifically for the fanfiction, perhaps an ancient witch who has been watching over the wizarding world since its inception.