First, IHO( International Hydrographic Organization), the official institute that announces the name of seas around the world, announced that 'East Sea' is the standard title for that part of sea. Thus, due to announcement of IHO, the official name for that part of sea became 'East Sea' internationally.
Secondly, 'Takeshima' is not a correct name for 'Dokdo Island'. As Dokdo Island is definitely Korea's territory it should be written as a name that is used in Korea. And also as the name 'Dokdo Island' has been called use for a long time, it should also be written as 'Dokdo'.
In short, the official names for sea and island is 'East Sea' and 'Dokdo'.
So I hope that you change the map image into another one that has 'East Sea' and 'Dokdo'.