My wife had a first name and a last name, with no middle name. She moved her last name before marriage to become her middle name, and took my last name as her new last name. So instead of Alice Baker with no middle name, she's now Alice Baker Helper.
When we went to Social Security, I took our marriage license and her passport with us. We told Social Security we wanted her name to appear as Alice Baker Helper. She already had a Social Security card as Alice Baker with the "DHS Authorization" stamp on it because she was here on an F-1 student visa and working part time for the college. Her new Social Security card had the new name on it (without the DHS stamp), and we used it for everything else including tax returns and driver's licenses.
Pick what you want the final name to be and use it on everything you fill out. Just pay attention for things like "Other Name(s) You Have Used Since Birth" and write out the original full name with all four elements.
Worst case, on the N-400 application there's a space for "Would you like to legally change your name?" We didn't use it because DHS already knew her by her new name.
Regards,
Vicky's Mom
