Well, in OTL we have:
Father Christmas (aka Pere Noel) in England and France (This character has picked up a lot of traits from Santa Claus, and vice versa, but they were originally distinct characters)
The three wise men, called Kaspar, Melchior, and Balthazar (those names have various spellings, and do not come from the Bible), in countries in which January 6 is the main gift giving day, such as most Spanish speaking countries.
Grandma Epiphany, called Baboushka in Russian or Befana in Italy
Santa Lucia in Sweden
The Yule Goat and also various elflike creatures called Tomte or Nisse in many areas of Scandinavia (including Finland)
The Christchild, called Kris Kringle in German, can be portrayed as a male or a female (sometimes Kris is said to be short for Kristine)
Saint Nicholas was an important saint to the Dutch. They still celebrate his feastday on December 6th (which I think is still the main gift-giving holiday). When Dutch settlers founded the city of New Amsterdam in the colony of New Netherland, it took a couple weeks for the cookies and things to get from the Netherlands to the children in the Dutch colonies, so in New Amsterdam they started celebrating the visit of Saint Nicholas on Christmas instead. Santa Claus is simply an adaptation of the Dutch for Saint Nicholas (You can still meet folks named Claus or Klaus).
Of course New Netherland and New Amsterdam were all conquered by the British, who renamed both the colony and its capital city "New York". A lot of British settlers then moved in, and brought British saints like St. George of England. Some time later, particularly during the revolutionary war and the War of 1812, it became unfashionable to be English in America. Fortunately, Washington Irving stept up to the plate with his book "Dietrich Knickerbocker's History of New York" which reminded the people of New York that they were not English, but in fact Dutch, and so St. Nicholas was their true patron saint. All the people of New York then embraced St. Nicholas and the custom of his visit on Christmas. And this custom then spread to the rest of the United States. And with American economic dominance of so much of the world, Santa Claus has spread to many other countries.
I think it is certainly possible to imagine things going differently in an AH!
KEVP