Some suggestions for choosing a name include naming the elf after a favorite candy, a name of a character from a favorite book, a word in a favorite song or a word unique to the family. Creativity and humor are common elements.
Another suggestion is having children close their eyes and naming the elf after the first thing they see when they open their eyes. Many elves have a first, middle and last name so that more than one person gets a choice in naming the elf. The Elf on the Shelf blog also features a list of the 20 most popular names for those looking for inspiration.