It doesn’t say it was named Classic Mac OS. It says “succeeded the classic Mac OS”. That does not imply they named it “classic” anything. The word “the” being present actually explicitly means Apple did not name it “classic”.

And I’m going to need a source on it being OS X 1.0. I lived through it and my memory as well as everything else says it was 10.0, 10.1, 10.2 etc.