I've only done a few gifts at this point. But I use my woodburner and burn my signature, the date, and occasionally a small message. For instance, my father in law passed away last May and I woodburned a memorial plaque for every member of the family..............bibles, sobbing angels, jesus, etc... On the back I wrote "In Loving Memory of Tom Brumley (my father in law) and his birth and death dates and a small bible verse about loss. I wanted to create a memory to make everyone smile everytime they read it. So it really depends on what the item is, how large, whether it's for sale or a gift, etc...
I think if I were to do sale items I would create a small logo with my name, address and phone # and print it on a tiny label or use a branding iron. Or possibly I would just sign it with my signature and the date. I guess I won't know until the time comes lol.
Christina