Everyone who is saying that the whole town is crazy is wrong. It's Moe-chan that makes people crazy, notice how all those people were normal reacting to Shamurin and only went insane when they saw Moe-chan.
It's Moe-chan alone that makes people around her into crazy cat ladies
So . . . either those people somehow learned Moe-chan's name by telepathy, or they independently decided that since she's so moe her name must be Moe-chan.