Just because a country calls itself something doesn't mean it's true.
Point of fact, the Democratic People's Republic of Korea is said to have four false statements in its name:
- It's not democratic, as nobody gets to vote on anything;
- It's not in any way shape or form "of the People"; only the Chairman's wishes matter and his word is law.
- It's not a republic -- it's a textbook example of a hereditary dictatorship.
- It only covers North Korea, not the entirety.
As the other answers point out, this isn't uncommon behavior, especially among oppressive regimes that see propaganda value in asserting the claims -- back when Germany was still split up, the communist-ruled eastern part named itself the "German Democratic Republic" despite again being none of those three.
More generally speaking, as a rule of thumb if a country or organization uses any of the phrases "for the People", "freedom", or "Patriotic" in their title, I recommend you get away from them as fast as prudent.