Can I use this loophole to get Social Security to change my name?

Yes, it is worth a try. When I got married, I took my marriage certificate to the DMV, they changed it to my married name, kept my maiden name hyphenated, and added his name, and took my Driver's License to Social Security and they changed it, no problem. It is worth a try. You know almost everyone there will give you a difference answer, so if it doesn't work the first time, try it a different day, or get into a different line. I've called them on the phone one time about a question and got like 10 different answers from 10 different people. They are all messed up.