In most world maps and atlases used internationally today, the Sea between Japan and Korea is indicated as the "Sea of Japan."
It is interesting to review the historical background of the dual use of "Sea of Japan" and "East Sea" by neighboring countries and other Western countries in the past.

Korea has used the term, "East Sea" in writings since 59 B.C. Reference to the "East Sea" was also constant in numerous maps created after the 18th century. Many geography textbooks published and used before the annexation of Korea by Japan in the early 20th century referred to the "East Sea," "Sea of Choson" or "Sea of Korea."

Russian maps of East Asia were all created after 1639 when Russians first arrived in the Pacific coast region. In 1687, Nic Witzen's "Noord en Oost Tartarye" refers to the East Sea as "Oceanus Orientalis." N. Goman's 1725 map uses the term "Eastern Ocean," and in a 1734 map, I. Kirilov refers to the East Sea as "Vostochnoe," meaning "east sea."
The Map of Asia printed by the renowned Petersburg Academy of Sciences in 1745 also refers to the East Sea as "Koreiskoe Mope," or "Sea of Korea." Other famous maps printed in Russia from 1745 to 1791 use the term "Sea of Korea." Adam Johann von Krusenstern (1770-1846), the Russian who explored the East Sea called it the "Sea of Japan" as did the French explorer, La Perouse (1741-c. 1788), who explored the East Sea in 1787.

However, the Russians called the East Sea the "Sea of Korea" in their last officially published map of 1844. Thereafter, it appears that the Russian Navy and numerous maps followed the European style in making geographical references.

Europe - The map which was created by Godhino de Eredia of Portugal in 1615 was the first map published in Europe to have called the East Sea as "Mar Coria" (Sea of Korea). The first obtainable map with the East Sea is called "Mare di Corai" (Sea of Korea) was published by Sir Robert Dudley in 1647 "Carta Particolare della Isola de Giapone" which was made in England.
The "Map of Asia" which appears in E. Bowen's World Atlas in 1744 and 1752 also refers to the East Sea as the "Sea of Korea."
The Map of the North Pacific published by J.N. Delise of France in 1750 after his exploration of Northeast Asia also calls the East Sea "Mer De Coree." Furthermore, "Sea of Korea" appears in the first edition of the 1771 Encyclopedia Britannica.

Dual naming
Finally, some mapmakers mentioned the names of "Mer du Corée" and "Mer du Japon" for the same Sea on their maps. One excellent example is the world map "Le globe terrestre representé en deux plans-hemispheres" published in Paris 1770/1779 by Nolin / Crepy.
Recently the Virginia Governor signed the "East Sea dual naming bill" into law. The bill, which takes effect on July 1st, requires all textbooks in the state of Virginia to say the waters are known by the Korean name "East Sea" as well as the Japanese name "Sea of Japan."

The Organizing Committee of the International Seminar on Sea Names has a good overview of the different papers published from 1995-2012 about the subject.