Cane here to say the same thing, e.g. https://en.m.wikipedia.org/wiki/Inverkeithing_High_School
Although, there's a subtle difference vs US usage: in Scotland High School is only used in the context of the name of a specific school, not as a term for the generic concept. E.g. "What secondary school did you attend?"; "I went to The High School" (meaning the Royal High School in Edinburgh). You'd never say "What high school did you attend?".