Use the last name on the ITIN. Unlike an SSN, which can be changed with the SSA by presenting the marriage certificate, the ITIN requires more work. You can contact the IRS with the last name update, and they can advise you if sending in a copy of the marriage certificate is enough to make the change. Or, you could mail in your return to explain the change and request that her ITIN is re-issued. But the easiest is simply to file electronically using her last name on the ITIN letter, so your return can be accepted now. Then later, you can update it with the IRS. (Her last name does not need to be legally changed with the IRS for you to file a joint return).
By the way, congratulations on your marriage!
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