Corrected @ Question: Adjustment of status

I recently got married to an American citizen. Before marriage, my status was f-1 student. Now that I am married, I must do the adjustment of status paperwork.
Question: My marriage certificate shows my name and my hu*****and's name but nowhere does it state that my last name is now my hu*****and's last name. On the adjustment of status paperwork, if I send a marriage certificate with my paperwork, do I use my last name as stated on the marriage certificate or do I use my hu*****and's last name now that we are married?