What does “…HAD me for secret Santa” mean?

Secret Santa is a thing where people in a group are given a random person's name and have to buy a gift for that person. She's asking who was given her name.

Secret Santa is something where a group of people all randomly draw names to get anonymous Christmas gifts for. If you "had" someone for secret Santa, that means you drew their name and were supposed to be getting them a gift.

Secret Santa is a gift-exchange tradition where members of a group are assigned the name of another member at random, and then buy that person a gift. She's asking who has\* her name and will be buying her a gift. (\*I hear "tell me who *has* me" rather than "tell me who *had* me".)