For those (like the author) who wonder why such a weird mishmash of different conventions was used to come up with the DACH abbreviation, it's because the word "dach" means "roof" in German, so there's a lot of wordplay that's done to talk about all these different regions which are 'under one roof'.

"Dachsprache" (roof-language) is actually a term used by some linguists (sometimes translated to umbrella-language) to refer to a dialect that becomes the standard language of a large region with a varied dialect continuum. E.g. the dialect of Florence became the "dachsprache" of all of Italy.