I am the GM for a small start up company. I applied for various business credit cards under the company name but with me as the primary account name

You would want to review the contract to see if you personally guaranteed the loan. Most loans and contracts involving small businesses require a personal guarantee. If that is the case, then you can be held personally liable. You may be able to settle the debt for less than the amount owed, but if the debt is large, filing for bankruptcy protection may also be something you should consider.