Bill of sale will work just as well. Anything that shows transfer of ownership.
Name the gun just for goodness sake don't carve it in the stock. Krp will kill you and then we have to go all through the mess of bail and life instead of capital punishment.
The old 7mm mag I have had somebody's initials carved in the stock and that was the first thing I did was buy another stock and get rid of the Remington stock. It had BWS and 4 notches carved in the bottom of stock below the ejection port. The only thing I could figure is somebody named Billy Wayne Smitherman either shot 4 deer or 4 of his neighbors. I never could figure which. Of course you can't shake a stick down here without hitting a Billy Wayne Smitherman or a Billy Bob Minor or even a couple of Joe Earl Ropers. I even know a Bo Joe Varden.