According to the map of your website, the sea between Korea and Japan is named 'Sea of Japan'. However, instead of using the name, Sea of Japan, it is more correct to use the name, East Sea.
To begin with, there are no historical nor political evidence that proves that the sea belongs to Japan. The sea is surrounded by other countries including Korea.
In fact. the name 'East Sea' has been used by Koreans for approximately 2000 years, and has been recognized internationally until the early 1900s. 'Sea of Japan' is the product of Japanese imperialism, and there was no mutual agreement between Korea and Japan to use such name.
Therefore, I highly recommend you to call the sea as East Sea, or at least to simultaneously use both names.