I signed a contract that my girlfriend entered into agreement with. She applied for the acoount alone. My name is not on the contract but when they delivered the goods she was busy and so I signed my name to her contract. Am I legally responsible to repay the debt?

If you agreed to the terms of the contract by signing it, yes, you are bound by it.

But it sounds like it was a contract for sale of goods. The goods were shipped to her. When they arrived, you signed a receipt. A receipt would be something other than a contract, something not binding you for payment. Whether the case depends upon the wording of what you signed.

It depends on what you signed, if you merely signed a receipt that shows the goods were received, then you should not be obligated. If you actually signed and agreed to the contract, and you signed and she did not, you are obligated and she would not be.