Yes, I'd add that even if OP is not trying to follow that particular convention of the books, an interesting name would evoke something of the school's history and even its English name would be a translation of the real name in the local language, so knowing where it is in the world would be important.Aside from Hogwarts, the other wizarding schools' names are linked to the country they are located in, almost stereotypically so - so, whereabouts is the school in your story?
It’s in ScotlandAside from Hogwarts, the other wizarding schools' names are linked to the country they are located in, almost stereotypically so - so, whereabouts is the school in your story?
in that case I'd go with Oilthigh nan Cailleach - Univeristy of Cailleach*It’s in Scotland