Dokdo is korea's cultural property.
However from 19th century, Japan keep insisting that Dokdo is their land and started to use Takeshima instead of Dokdo. Reasons why Japan says Dokdo is their land is because they found it first and nobody was living there when they first found it. However from historical data, it is easy to find that there is a record from 16th century in which Dokdo was painted. Also, from Sanfrancisco treaty in 1952, it is said that Dokdo belongs to Korea.
Therefore, Dokdo is explicitly Korea's territory and it should be called as Dokdo instead of Takeshima.