Your return should not be rejected if you use your married name on the return. The IRS matches your information with SSA. Therefore, if you made the name change with SSA, then this is the name you should show on your return.
See the extract below from the IRS website regarding the name change:
"When you file your return, check that both your name and SSN agree with your social security card to prevent any delays in processing your return and issuing any refunds"
Name Changes & Social Security Number
Here is another useful link on married filing jointly
Married filing jointly or separately
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