For fantasy stories, some school name ideas are: Moonstone Academy. Moonstones are often associated with magic in fantasy, so this name gives the school an air of mystery and magical power. The Twilight Tower School is also a good option. 'Twilight' has a sense of mystery and the 'tower' makes it seem like a place full of secrets and hidden knowledge. And finally, there's the Silvermist School. The 'silvermist' gives the impression of a place that is a bit otherworldly, perhaps surrounded by a magical mist where all kinds of strange things happen.
In a fantasy story, names like Celestial Spire School are great. 'Celestial' refers to the heavens and 'spire' gives the idea of a tall, grand building reaching towards the sky. It could be a place where students study magic related to the stars. Then there's the Whispering Woods School. It sounds like a place where the woods around the school have secrets and perhaps talk to the students. Also, consider the Phoenix Rising School. The phoenix is a symbol of rebirth and magic, so it would be a very fitting name for a school in a fantasy story.
Dragonfire Academy. It immediately makes you think of a place where there might be dragons and magic related to fire. Another one could be Enchanted Grove School. It gives a feeling of a place full of magic and mystery, hidden away in a grove. And then there's Mysterium School, which is very mysterious and could be a place where students learn all kinds of arcane knowledge.