There is no such thing as "registered in your name" here in Indiana. In face to face transactions you have no duty to record the transaction whatsoever. Some people prefer to do a bill of sale and yet others will require an LTCH as a poor man's background check before doing a face to face.
There IS GUN REGISTRATION in many communities around the US, but nothing federal. Toledo, Columbus, and Cleveland Ohio are examples although there has been a court case or two recently challenging their gun registration. Not sure of the status.