The goddess could be an ancient Celtic deity. In the fanfiction, the author might choose a Celtic goddess because of the rich magical lore associated with them. For example, Morgan le Fay from Arthurian legend could be reimagined as a goddess in this context, and she could adopt Harry due to her interest in powerful magic users.
Well, it could be that the goddess, perhaps a powerful magical being from an ancient realm, takes Harry under her wing. Maybe she sees his potential and decides to protect him from the dark forces in the wizarding world that Voldemort represents. She could teach him unique magic that no one else in Hogwarts knows, giving him an edge in his battles.
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.
The goddess could also be an original creation for the fanfiction. A being with a unique set of powers like the ability to control time and space. This goddess could be betrothed to Harry to stop an impending doom that threatens both the wizarding and Muggle worlds. Her powers would be so great that she needs Harry's connection to the wizarding world to fully utilize them and save the day.
It could be Athena. Athena is known for her wisdom in Greek mythology. She could pass on her wisdom to Harry, making him not just a powerful wizard but also a very wise one. He could use this wisdom to solve problems in the wizarding world in a more strategic way.
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.
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.
It could be Athena. She is known for her wisdom, and Harry has shown great intelligence throughout the series. Maybe his strategic thinking and ability to solve complex problems come from his connection to Athena.