The initial version of a Secret Santa name-picking app for my family, which has since become a web app.
This limited, buggy version of GiftDraw for Android lets you add people, put them into groups (members of the same group will not be assigned each other's names), and then randomly assign two recipients to every giver with one touch. (To redo the assigning process, you will currently need to manually clear the app's data through Application Settings.)
GiftDraw for Android requires that ActionBarSherlock be included as a library project in order to compile. At the time I was last working on it, GiftDraw was using ABS 3.4.0, though more recent versions may work.
ICONS CREDIT: Some icons in GiftDraw for Android are from the Christmas XP icon pack by Jojo Mendoza.