For a while it was even visible on both sides of the Korean peninsula: a left-wing military dictatorship in the North referred to themselves as the "Democratic People's Republic of Korea", while a right-wing military dictatorship in the South referred to themselves as the "Republic of Korea". Neither country actually operated as a republic, but both seemed to like the term (and did have some superficial trappings of a republic, like legislatures). The South is now an actual Republic, though, since around 1987.
Similar situation for some years in the Taiwan Strait, where the not-a-republic People's Republic of China faced down the also-not-a-republic Republic of China (Taiwan).
Right. It's kind of seen as a "given" now that South Korea and Taiwan are the democratic, American-friendly, "good guys" and the DPRK and PRC are the authoritarian, oppressive "bad guys," but back in the '60s through the '80s before the ROK and ROC democratized, the situation was much murkier. Because of the Cold War, those regimes were considered allies solely by virtue of not being Communists, but they were also very unfree. Perhaps the winding down of the Cold War had something to do with their falling out of power and being replaced by democracies.
Similar situation for some years in the Taiwan Strait, where the not-a-republic People's Republic of China faced down the also-not-a-republic Republic of China (Taiwan).