an arrangement in which each person in a group buys a Christmas present for one other person, without the person knowing who bought the present

Do you want to be in the office secret Santa? 你想参加玩办公室神秘圣诞老人游戏吗?

I need to buy a secret Santa gift. 我需要买一个神秘圣诞礼物。

a person who buys a present in this arrangement

I wonder who my secret Santa was! 我想知道我的神秘圣诞老人是谁！