The term “People’s Republics” can be dated back to the country’s formation when Moscow was spreading socialist values to its satellite states.
Korea had just been liberated from Imperial Japan in 1945 and was being split in two by the allied victors after the Second World War. The short lived People’s Republic of Korea was established in the South. The Soviet propped Northern side quickly added “Democratic to it’s title to differentiate itself. It has not changed it’s name ever since.
Democracy in this context clearly does not mean democratic elections, free speech etc like we’re used to – but rather that the party, in this case the Worker’s Party of Korea – represents the masses as opposed to a capitalist or colonial system.