1. What does it mean?
손민수 refers to a character in Cheese in the Trap known for copying another person's style. 손민수하다 now describes following someone else's fashion, purchases, or choices, including a fan buying what a favorite celebrity uses.
Also written or said as sonminsu
2. The nuance
It can be playful admiration or a complaint about intrusive copying. In an ordinary news item it may simply be a person's name; do not assume every mention is slang.
3. Examples
“가수가 쓰는 모자가 마음에 들어서 손민수했어.”
I liked the hat the singer wears, so I got the same one.
“친구와 취향이 겹친다고 무조건 손민수라고 하긴 어렵지.”
Sharing a friend's taste doesn't automatically mean you're copying them.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.