I dont know... but I just baught a Mossberg 500 shotgun a couple of days ago under my old name. Why would I do that you say? Because even though I am a US citizen, how I came to be one is by government cock-up. So, as a result, my changing over of legal documents came to a grinding halt because Indiana BMV will not accept my british deed poll papers. But, the reason I bought the shotgun was to A. See if I can pass a background check and B. Buy a weapon for home defence. Things do seem to be getting a bit screwy these days after all. But I think it proves that the background check just makes sure you dont have any outstanding warrants, prosecuted for anything illegal, etc. However, if your social security card has not been updated with your new name then yes, you should put down your old name. Once you get it changed, then I dont see why you need to put down your old name. Get it changed before you get a US drivers license. It will save you a big fat headache.