Recently the Yomiuri News reported the following:
South Korea media were unanimously repulsive as "The government had shown a lack of diplomatic effort" regarding US State Department's repelling the use of parallel description of "Tokai (Donghae)"; the South Korea government was showing a mixed reaction.
South Korea after obtaining independence in 1957 joined the International Hydrographic Bureau (at present the International Hydrographic Organization = IHO); since 1992 it began to insist that the English marking of "Tokai" be used internationally. It insisted that in South Korea on grounds that it was on the east side of the Korean peninsula "Tokai" was called as a custom, and "it is irrational to assume the high seas with a name of a country, and should describe the Sea of Japan with Tokai in parallel".
In South Korea, there was an understanding that "It was in the first half of the 20th century that the name of the Sea of Japan was popular in the world, when they were under the colonial rule of Japan". South Korea linked it to the history question, same as the Takeshima (Shimane Prefecture) problem that both Japan and South Korea were insisting on the sovereignty right.
I hope the argument in using the name " East Sea" or "Sea of Japan" would not hurt the relationship of these two countries.