The correct name of that sea is East Sea. And now, I'm going to tell you why Sea of Japan is wrong name and East Sea is correct name.
A long time ago, the Korea and Japan accepted that sea between two countries was named as East Sea and many old maps were marked that sea as East Sea.
But, in 19c, when Imperialism were spread in the world and japan, Japan annexed Korea by force and illegal, they changed name the sea's name to Sea of Japan. Nowaday, Korea has independant from Japan, so it's right that the sea's name should be changed to the right name.