I have a branding iron. I usually brand on unfinished wood because I will brand the back of the backer which I do not finish,,,,, should I? I have also branded a piece of veneer several times and I can cut off a piece with the brand on it and glue it to a piece. If you cut it nice it looks pretty good. My branding iron is one you heat by torch and it takes some practice to get it heated just right and evenly. That is the reason I branded a piece of veneer several times. When I have it heated correctly I want to brand more than one thing... So I hit the veneer. Then I don't have to heat it for each project.
I have not tried an electric one, maybe more convenient, but somewhat more expensive.