happaku (八白, i think) elementary comes from 嘘八百 ("uso happaku"), meaning a great amount of lies or something said being completely made up of them. they shouldn't have named the school that because now everyone who goes there is going to lie.
doya-kun has such a doya-gao

is the teacher's name actually "atarashii" as a pun on her being the "new" teacher after their old one got replaced? im wondering because when i read some chapters in the past, i dont remember that being her name, but its not like teachers really get actual names in kids manga anyways. otherwise this feels like "just according to keikaku" to me.