Here’s a tip I got from a child’s birthday party a few years ago, and have used ever since.
As the children gather for the official opening of the presents, have special seats for the birthday child and the gift giver(s). And before each gift giver pops back to his or her seat among the throng of curious little onlookers, snap a few photos. They will be a reliable record of which present came from which guest! Plus, it’s nice to have a photo or two of that sweet moment of giving shared between friends.
Have a lovely day!