What is the Korean name for a first degree black belt?

The color black is gamjang 검정 (pronounced "gahm - jahng")

The Korean Word for belt is ddi 띠 (pronounced "dhee")

Therefore, a Black Belt itself is called gamjang ddi 검정띠

"Degree" or grade level of the adult Black Belt is dan 단 (pronounced "dahn")

A person who holds the Black Belt rank is called a

yudanja 유단자 (pronounced "you - dahn - jah")