The Japanese name of the manga is "Himekishi wa Barbaroi no Yome". Its literal English translation is "The Princess Knight is the Barbarian's Bride". But the official English name for the manga is "The Barbarian's Bride" in North America. The anime has the same Japanese name as the manga. But the official English name for it is "The Warrior Princess and the Barbaric King" according to Crunchyroll.
