In the movie "Red Dawn" where the invaders set up a base in a small Colorado town, one of the first orders the new commander issued was to go to the gun stores and collect the "4473s", the yellow form every buyer has to fill out when he buys a gun from a dealer. The dealer must keep those forms on file forever or until he goes out of business, when he is to forward them to the BATFE.
Since the ATF can come inspect a gunstore and the records therein at any time, there have been plenty of reports of ATF employees simply entering all the 4473 data into portable computers, probably for uploading into a national database. If you bought it from a dealer Big Brother knows about it.
Even if you buy it from a private party it can probably be traced to you since that private party needs to cover his -- er -- assets if an investigation is conducted. It may seem wrong in many respects, but the only gun you can buy and be reasonably certain it won't be traced is a stolen one.
In the case of the paperless guns I have, the seller did not know me, nor did he take my name. I did buy one other pistol that way, but sold it to my father in law. It's still in his gun safe AFAIK, although it did get lots of use those first few years after he bought it.
There was a family owned gun-store back home where grandpa had a bad habit of dozing off while doing the paperwork and dropping his cigarette into the files. I can recall 2 or 3 fires where most of the files where lost. Fortunately, their office was built from fire-rated materials and nothing except some old forms were lost.