Business cards are issued to individuals, not to businesses. You will provide a SSN when you apply, even if you use an EIN. Apply as a Sole Proprietor using your legal name, do not add any words to your name, do not use a company name or EIN -unless- the business is registered in your state. Chase will seek to verify the registration in public records, and the application will fail if they cannot find it.

It makes no difference how you use a business card.