"Gift exchange" refers to a process where people give and receive presents as a way of showing appreciation or celebrating a special occasion. Full definition
Favorite holiday memory / memories: doing white elephant gift exchanges with friends — the presents and the process are always a riot! (thechrisellefactor.com)
Instead of spending $ 15 on a white elephant gift exchange where everyone may or may not end up with something useful, have everybody bring a kid's book to donate. (policygenius.com)