My children named him, Chippy.
We are having fun "playing" elf on the shelf and Santa. My children know that Christmas is really about Jesus and His birth. They know Santa is not real, but we don't over stress it. We have friends who do not do Santa at all and others who do tell their children he is real. It is up to each parent, and we have fun playing Santa.
Today, Chippy decided he wants to watch mommy's favorite Christmas movie (good job Chippy!)