1. What does it mean?
닉변 shortens 닉네임 변경. It describes changing the name shown to other users, whether in a game, community, or social account.
Also written or said as nikbyeon
2. The nuance
It does not necessarily mean creating a new account. What else changes, and whether old names remain visible, depends on the service; the slang itself makes no promise about privacy.
3. Examples
“닉변해서 못 알아봤구나. 지난주에 같이 게임한 사람이야.”
You didn't recognize my changed nickname. I'm the person you played with last week.
“계절마다 닉변하기보다 이번 이름을 오래 써 보려고.”
Instead of changing names every season, I'll try keeping this one for a while.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.