How can you get a handed down firearm registered in your name?

A good first step will be to check with a gun dealer in the area where YOU live (we don't know that, since you did not specify). MOST states in the US do not have "registration" of firearms, other than machine guns. SOME do, and the process varies from state to state. We also have questions here from around the world- and the process is different for England and Alabama.