Name the list and pick its rules. Then you invite the others from its page.
Everyone writes a letter to Santa. In the draw each person gets someone else's letter and buys that gift; nobody draws their own. Until the draw people can join and write letters; after it, nobody can join.
Once the list is set up, on its page you can pick pairs who do not draw each other, e.g. spouses.
With the name hidden there is a second day: the gift sack opens and the names show up.