You don’t need ID to buy a gun in the US.
Private transactions are completely paper and record free. (Unless you are from some non-flyover state.)
It’s only when you sell guns as a dealer that you are required to get ID and whatnot from the purchaser. (Even then, there is no penalty for BUYING the gun without ID; the penalty attaches to the SELLER.)
It’s only when you sell guns as a dealer that you are required to get ID and whatnot from the purchaser. (Even then, there is no penalty for BUYING the gun without ID; the penalty attaches to the SELLER.)