It sounds like you need to make a separate account in your own name. There is probably nothing you can do about the past transactions.
You need to report the income on your tax return no matter whose name the account is in. If you file a joint return with your spouse, it won't matter that the SSNs don't match. If you file separately, you still must report the income. The IRS will probably send a letter to your spouse asking why he did not report the income. He can reply with an explanation and a copy of your tax return showing that you reported the income.
