Christmas was introduced here ( in a major way ) by the department stores about three centuries later than it was introduced ( in a minor way ) by the earliest Christian missionaries.
Of course, the latter didn’t mention Santa Claus… I mean Santa-san.
“Traditionally”, Japanese people buy Christmas cake ( a fresh-cream layer-cake with strawberries… they think it’s an American tradition ) on Christmas Eve as a dessert to follow another American Christmas tradition: a bucket of Kentucky Fried Chicken ( I am not making this up! ). Little kids get a present from Santa-san. Young couples go out to dinner and then to “Love Hotels”.
I don’t have a cite yet, but statistically, for the past 30 years or so, the dates on either side of September 26th are the most common birthdates in Japan…
They’re Christmas babies!
Everyone tilt your heads to the side and say,
“Awwwww!”
As for the OP’s “Happy Annual Gift Day”…
Japan has a traditional winter gift-giving season called o-seibo, during which one gives gifts to one’s boss, teacher, family doctor, landlord, etc…
Gifts are often daily necessities, like canned food, fresh fruit, fresh seafood or meat, cooking oil, bottled and canned beverages ( tea, coffee, beer, sake… ), soap or detergent, … you name it.