How to remove label from sink without damaging the sink?

If you can get under an edge of that label, try sawing it off with some dental floss. You'll still have a stick residue to deal with, but there are products that can remove that without leaving a mess.

Razorblades can be dicy with porcelain - it's possible to scrape metal off into the ceramic surface and leave a mark that's difficult or impossible to get out.

I'd start with heat - somewhat gently (no thermal cracking, please) such as a hair dryer, and either a plastic puttyknife (if you want to buy a tool) or sanding an edge on an out-of-date credit card (if you'd rather not buy something you can make) to pry the label up once you get the adhesive warm. Depending on the adhesive, heat may make it release very easily.