The sea between the Korean Peninsula and the Japanese Island, called as Sea of Japan in your map, is also called as 'East Sea.' To prevent international dispute between Korea and Japan, it is right to both mark 'East Sea' and 'Sea of Japan.'
In 1910, Japanese Empire invaded Korea and took control for 36 years. During this domination, Japanese Empire force to mark the name 'Sea of Japan' instead of inherent name 'East Sea.' Since Korea recovered sovereignty and is independent nation now, it is reasonable to reject using 'Sea of Japan', which symbolizes imperialism and painful history to Korean. If it is hard to change the expression in an instant, it is necessary to mark both designation at the same time.