The Sea of Japan and Koreans
The Sea of Japan is a nearly closed body of water, surrounded by the Asian Continent and the Japanese Archipelago, shared by Japan, Korea and Russia, connecting with the East China Sea, the Pacific Ocean, and the Sea of Okhotsk through the Korea Strait, La Pérouse (Soya) Strait, the Tatar Strait and the Tsugaru Strait.
The name "Sea of Japan" fits its geographic position. The sea is characterized by the Japanese Archipelago, which divides the body of water from the Pacific Ocean. Without the archipelago, there would be no geographic feature to be named.
Koreans, however, claim that the name "Sea of Japan" is wrong and should be changed back to the East Sea, the English translation of the Korean name "Dong Hae," although it is located to the west of Japan and to the south of Russia. They think the name after one nation is unacceptable, even though the strait between Japan and Korea is called "Korea Strait."
I will explain problems in Korea's claim.
Koreans assert, "The name East Sea, besides its neutral character, has an additional advantage in that the adjective East perfectly fits with its geographical position, located in the Far Eastern part of Asia." (*) You will find they covering in whitewash the fact that the name "East Sea" is the English translation of the Korean name and used only in Korea to refer to the Sea of Japan. What are located to the east of the Asian Continent are not only the Sea of Japan but also the East China Sea and the South China Sea, and these seas are called 'East Sea' by Chinese and Vietnamese respectively.
In China, the East China Sea is referred to as "East Sea" ("Dong Hai"  in Mandarin Chinese). The name "Dong Hai" has already registered as "East China Sea (Tung Hai)" in The Limits of Oceans and Seas published by IHO. ("Tung Hai" is another romanized form of Dong Hai) (See: Cross-Reference List of Hydrographic Data Codes)
Vietnamese name of the South China Sea is Bien Dong, which literally means East Sea. (Bien = Sea, Dong = East) They also use "East Sea," the English translation of Bien Dong. For example, the Vietnam Ministry of Foreign Affairs says, "The coast stretches more than 3000 km, along side the East Sea of the Pacific Ocean." (*)
Japan is a special case. Japanese used to vaguely call the Pacific Ocean as Tokai, whose meaning is East Sea, since it is located to the east of Japan, but it is no longer in use. Instead, Tokai indicates the Pacific coastal region. The name of Tokai is considered the abbreviated form of Tokaido, an ancient province of Japan. It is worth noting that for the Japanese people the word "East Sea" indicates the other side of the Sea of Japan. It is one of the reasons that Japanese strongly oppose the name of East Sea. Who does not get confused if both sides of the nation are called the same name!
Now I have to explain the influence of Chinese characters on East Asia. Chinese characters with a lot of Chinese words were imported to Japan, Korea and Vietnam. Although Vietnam and North Korea abolished the character, a great number of Chinese word are shared. The ideographic characters maintain uniformity in spite of the different pronunciation. Thus the characters corresponding to the East Sea are identical. They are pronounced as "Tokai" in Japanese, "Dong Hai" in Mandarin Chinese and "Dong Hae" in Korean and treated as the same word. But as I described above, they point to different places in different languages. So adopting "East Sea" gives Chinese and Japanese a good deal of trouble.
The name of "East Sea" is used not only in East Asia but also in Europe. The Baltic Sea is called "East Sea" in Denmark, Germany, Finland, Netherlands, Norway, and Sweden. By contraries the Estonian name for the Baltic Sea means "West Sea".
In this way, the name "East Sea" does not indicate single place. "East Sea" is used all over the world (see a list of the East Sea.) It is not the Sea of Japan that more than 1.6 billion people call "East Sea"! An official name for a geographic feature is translated into each language. For example, the Japanese name for the Red Sea is "Kokai" (Ko = Red, Kai = Sea), and the Sea of Japan is called "Bien Nhat Ban" in Vietnamese (Bien = Sea, Nhat Ban = Japan). Therefore it is obvious that if the name "East Sea" become official, name collisions will occur in a lot of languages.
I do not think the history of the name is important as Koreans think, because the trouble Koreans made are serious enough to stop the Korean attempt to make the name "East Sea" official. But I cannot overlook Korea's false propaganda.
Koreans persist that the name "East Sea" had wide acceptance not only in Korea but in China, Japan and Western countries, and that Japan unjustifiably turned it into the Sea of Japan in the 20th century. But in truth, the name "Sea of Japan" was widely used in the 19th century around the world when Japan had not appeared on the international stage yet.
How could Japan have deleted what had never existed? Almost no Western map shows the Sea of Japan as "East Sea". Why Koreans insist that the name "East Sea" had widely used in Western countries? It is because they equate "Oriental Sea" and "Sea of Korea" with "East Sea". The only common point is that they are not the name "Sea of Japan". In addition, what is shown as "Eastern Sea." in historical Western maps is the East China Sea rather than the Sea of Japan. For more information, see this page.
The first map with western knowledge of geography in China, called "Kun Yu Wan Guo Di Tu", was made by an Italian Jesuit priest Matteo Ricci (1552-1610) in 1602. This is considered the first map that denotes the term "Sea of Japan" (Ri Ben Hai). The influence of this map on East Asia was so strong and a lot of copies were made in China and Japan.
Russian admiral Krusenstern made popular the "Sea of Japan" (Japonskoe More) in the West through the publication of his book in 1815. He circumnavigated the glove and published his memoir which translated into several languages including Japanese. And since the 18th century, almost all western maps denotes "Sea of Japan." It should be noted that Japan was closed off to the world until 1854. It is clear that Japan had no need to change the name.
There was no practice to name a body of water in large scale in East Asia. So every sea was called nebulously a name after its direction or a country across the sea. For instance, the Sea of Japan was called Hokkai (north sea), Bokkai (Bo sea/Bo Hai sea) or Chosenkai (sea of Chosen.) It is dubious that they were considered geographic names. They were common nouns rather than geographic names.
Thus the Sea of Japan was named by the Westerners as well as many other seas and oceans. It is nothing more than anachronism to make popular the local name reflecting ignorance about geography.