This is how I advise my clients to proceed, because your name cannot then be linked to the company. You have to watch some banks. They will want to put your company name and your own name on the same card which is undesirable. Best just your own name or better yet don't get any cards for your company account. Get a second personal account for your card and transfer between the two.
Debit cards are available in that form, or, indeed with no name embossed.
This is a necessary security rule. Imagine losing a card that could be used by anyone at all. It is in your interest. This is how I advise my clients to proceed, because your name cannot then be linked to the company. DGO is right.