As 'East Sea' and 'Dokdo' is Korea's territory, each of them should be written as 'East Sea' and 'Dokdo', instead of 'Sea of Japan' or 'Takeshima'. Their names should be written in this way for historical reason. Historically for 2000 years, not only in Korean maps but also in old Japanese maps, it was called 'East Sea', not 'Sea of Japan'. However, Japan ignored this historical background and just started to call it 'Sea of Japan' as if it is their territory. Thus, historically, the right way to call the sea is 'East Sea'.
Also, IHO( International Hydrographic Organization) regulates that world's seas should use standard international titles. And 'East Sea' is the title chosen by IHO. Thus, historically and internationally, 'East Sea' is the correct title for the sea.
Also, as Dokdo is definitely Korea's territory and historically has been called Dokdo for very long time, it should also be written as 'Dokdo' only, not Takeshima.
In short, for these reasons, the map should title the sea and the island as 'East Sea' and 'Dokdo'.