I rarely if ever sell firearms. On those occasions when I do, I typically record a bill of sale. The bill of sale records only the date and the other party's name, state and DL number (I don't care or need to know where he/she lives, but the DL number is a unique, traceable number). If a LEO comes a knockin' about a firearm that was previously in my possession, that information should be adequate for them to find the other party.
Once you transfer a firearm to another person, there is no way to know or control how it is subsequently used, and I don't think it's reasonable or practical to ask any private person to attempt to conduct a background check on such a transaction, but at a minimum I can at least give an LEO with legitimate investigatory need at least a jump start on locating the party to whom I transferred the firearm. I think that's enough.