Girls in Boxes
joined Oct 18, 2014
Why not simply say something like "Wait! This is the wrong Meibou Academy!!" or "Oh, do you mean the other Meibou Academy?" type things...? You don't really need to explain in any more detail than that she mixed up two schools with the same name for the joke to get across.
If this was in English and there were two schools called "St. Mary's Academy" (maybe one in one suburb, and one in the other) and you mixed them up, that's what you'd say, after all.