Currently the name Santa Claus is approximately 10 times more popular than Father Christmas in the United States, but there was a time when their popularity was similar. In addition, the popularity of those two names had tracked together in the UK until the mid 1980's.
THE ORIGIN OF AMERICAN CHRISTMAS MYTH AND CUSTOMS offers very good insights into Santa's current dominance in the USA:
About 1890 Santa Claus' modern Christmas role becomes established.
The first store Santa Claus was James Edgar, Brockton, Mass., 1890.
Mrs. Claus created by Katherine Lee Bates, Sunshine and other Verses
for Children, 1890 (ref?), violating sainthood celibacy restrictions.
Letter to Virginia (O'Hanlan), Francis P. Church, New York Sun,
1897--"Yes Virginia. There is a Santa Claus."
The image of Santa Claus now becomes varied and often elfin,
rejecting Nast's robust figure. The Oz illustrator W. W. Denslow drew
Santas of Munchkin-size. Arthur Rackham, an artist and illustrator of
children's books drew Santa as an elf.
Norman Rockwell drew full-sized Santas for the Saturday Evening Post.
Archie Lee of the D'Arcy Advertising Agency proposed a realistic,
modern appearing Santa Claus with red cheeks and wrinkled face, but
appearing vital and young, for Coca Cola. This image was painted in
oil by a commercial illustrator Hadden H.Sundblom, starting with the
1931 holiday promotion. The original model was Lou Prentice, a retired
salesman who died shortly thereafter. This is the Santa Claus we know
The name Santa Claus has become a well developed cultural icon, and we discover an intentional development in the article Santa Claus Does More than Deliver Toys, in the Journal Consumption Markets Culture pages 207-240:
Society's collective memory of Santa Claus reflects the dynamic and
interactive process between advertising, as well as other cultural
institutions, and consumers. Coca-Cola's advertising has maintained,
transformed and mass-produced the image of Santa Claus over time.
Consumers have numerous experiences with Santa Claus— they have
watched, listened, read, and even dreamed of Santa Claus. As consumers
experience Santa, they actively combine and adapt cultural discourse
to fit with their individual, familial, and cultural traditions.
The name Santa Claus benefits news papers, magazines, movies, merchants, politicians, and just about everyone in our country. Saint Nicholas is surely welcome in the United States, and we definitely prefer to call him Santa, but he has Nicknames too:
Santa Claus, also known as Saint Nicholas, Father Christmas, Kris
Kringle and simply "Santa..."
The monicker Father Christmas competes with Saint Nicholas, and is a more popular than either Kris Kringle or Saint Nick. Traditionalist can argue about whether it should be, but in the United States, Santa Claus and Father Christmas are both the mythologized historical Saint Nicholas.
Robert Ellice Mack wrote the iconic Old Father Christmas Picture Book in 1888 with an elfish picture of "Santa" on the cover, but the concluding stanza in the first poem reads:
Now wake little people dressed in white
Old Father Christmas came last night
He crammed your stockings--and children look!
He brought you a colored picture book!
A Santa by any other name is just as jolly!
A few decades later, Primary Education, Volume 13 contains a play where a letter is read:
Santa Claus Land, December 21, 1905
Dear Father Christmas:
Will you and your little band of workers give me some timely aid?...
At the peak of it's popularity, the name Father Christmas appeared in The Kindergarten-primary Magazine, Volume 33:
Father Christmas has a white beard and carries a bag.
The name Father Christmas is just as popular today as it was in 1922. Barbara Reeds published a Christmas story called *Father Christmas* in 1995. At Amazon.com the book, Father Christmas BC is among the many books available promoting Father Christmas as Santa.
Perhaps the most well known recent reference to Father Christmas is in the movie adaptation of C.S. Lewis's The Chronicles of Narnia: The Lion, the Witch and the Wardrobe (2005), where Father Christmas accosts the children, announces that Christmas has returned to Narnia and gives them powerful gifts that will factor into the rest of the stories. The fact that C.S. Lewis and J.R.R. Tolkien, who also has a popular book entitled Father Christmas, are British authors does not diminish their influence on American culture.
Father Christmas and Santa Claus were equally popular names in the British Empire that spawned the American dream, and so it is no surprise that both names were popular in the early days of the United States. Father Christmas has not become a less popular name, but cultural developments have made Santa Claus a more popular name.