Part of Speech: noun

Definition:foreigner, especially a person of Philippine, Korean, or Vietnamese

Source: Words at Dictionary

Choi Jeong Min by Franny Choi (Line 5)

“Already Knew to let my salty gook name drag behind me in the sand, safely out of sight”

The word “Gook” is a term used to express a foreign name especially a Korean, Philippine person. In the poem she expresses that her name is a very foreign Korean name.