Among English speakers who celebrate Christmas, shopping for gifts to give people is something that everyone has to do. It's like a job that everyone knows they have to do, but can sometimes be difficult. So you call it "(one's) Christmas shopping":
Have you done your Christmas shopping yet?
I still haven't done my Christmas shopping.
You can think of other phrases to describe this activity, like "gift buying" or "Christmas present buying". But "Christmas shopping" is the most popular way to refer to it.