If it is a corporate credit card and the card is in the corporation's name then generally you will not be liable for the debts incurred by the credit card.
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If the corporation defaults you can expect a demand for payment. The corporation should have its own tax ID number and thats what should be used, not your social security number and name.
By the way, your question says "my name" in bold and "cororations name" in the details.
You need to start paying more attention to corporate formalities. Even when you sign your corporation's name, you need to put your corporate title to indicate that you are signing in your corporate and not in your individual capacity.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Generally, a shareholder is not personally liable for the debt of the company. This is not always the case. When a corporation hasn't created credit, they might require that an owner provide their credit as a security blanket in case the company defaults.
I recommend that you look into what your responsibility is on that account and ask for it in writing.
The actual card should be in the name of the company noting you as an "authorized user". Sometimes, your name will appear on the card as well. For identification purposes, most credit card companies will require your Social Security number. However, the agreement for payment should be only between the company and the credit card company. You should NOT be required to sign an application binding you to pay if the company doesn't. Keep in mind, however, that unauthorized use of the card can open someone up to civil and possible criminal charges by the company itself.