[quote omitted for brevity: summary of the complaint is that we use "Sea of Japan" in the map on [[en:Japan]], but "East Sea (Sea of Japan)" in the map on [[en:Korea]]. Since the name is disputed, it is suggested that we use both names in both articles.]
The request seems reasonable to me, but given the image on [[en:Japan]], I have no good way of implementing it. It's a map created by a Wikipedian, but uploaded only as a raster image. To edit the caption in it would require some careful photoshop work and matching of typefaces.
If someone can manage to do it, I think the solution used on [[en:Korea]] is the best one: use the preferred name of the country the article is about primarily, but list other names in parentheses. So "East Sea (Sea of Japan)" on the Korean article, and "Sea of Japan (East Sea)" on the Japanese article. (I think a similar approach was suggested for the disputed name of a gulf near Israel.)
-Mark