The most common Korean word for “name” is 이름 (ireum). There is one more word with a similar meaning — compare them below. 「name」는 한국어로 이름.
name
TOPIK 1 · noun · honorific: 성함
name
TOPIK 2 · noun · honorific form of 이름 — use it for elders and customers
Words and levels: TOPIK I essentials (National Institute of Korean Language standard curriculum, KOGL Type 1) · examples: Cheesepotato