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It’s kind of hard to say. What does [name_f]Avalon[/name_f] have in connection to the school? The [name_f]Avalon[/name_f] school and [name_f]Avalon[/name_f] Academy could be either a random name for the school. The Academy of [name_f]Avalon[/name_f] sounds like the name of a school that’s in [name_f]Avalon[/name_f]. St. [name_f]Avalon[/name_f]'s Academy would a school named after a saint. Legends of [name_f]Avalon[/name_f] doesn’t sound like a school at all.
Based solely on sound, I voted the [name_f]Avalon[/name_f] Academy.
[name_f]Avalon[/name_f] is the island where [name_m]King[/name_m] [name_m]Arthur[/name_m] went when he was dying. I imagine that’s what the ‘school’ is named after/supposed to represent in this story 
I went for St [name_f]Avalon[/name_f] Academy because I would totally believe that was a school if I heard it in real life.
I would knock out Legends of [name_f]Avalon[/name_f] and The [name_f]Avalon[/name_f] School right away, they just sound awkward to me. [name_m]Saint[/name_m] [name_f]Avalon[/name_f] never actually existed so it depends on how realistic/historically accurate you’re looking to be. I would probably go with [name_f]Avalon[/name_f] Academy, plus it’s easy to give a nickname with the repeat letters (AA, double A, A squared etc.)
Since [name_f]Avalon[/name_f] is NOT the name of a saint, I would eliminate those options for inaccuracy. I think [name_f]Avalon[/name_f] Academy followed by [name_f]Avalon[/name_f] School would be the best options for your story.