I like asking questions like those above. I actually want to spend time next year researching many of the origins of Christmas traditions, particularly the pagan ones. I think it will be fun to write and I hope it will be fun to read. So if you're looking to shower me with gifts this season, I wouldn't argue for some reference material for the book.
So why is it called Christmas in the first place? Christmas is a compound English word with roots going back over a thousand years. Our current English word Christmas comes from the Middle English word Cristemasse. And Cristemasse itself is a derivative of the Old English Crīstesmæsse , a word first recorded in 1038. Crīst is an Old English translation of the Greek word Khrīstos(Χριστός--which we English speakers know as "Christ"), which comes from the Hebrew word Māšîaḥ(מָשִׁיחַ--which we English speakers know as Messiah) which means "anointed one." The word mæsse comes from the Latin word missa. Missa means "dismissal" and comes from the Latin phrase "Ite, missa est" which translates to "Go; it is the dismissal." Over time the term missa (and later mass) came to denote the entire Eucharist service in the Roman Catholic Church. So Christmas basically means "Christ's Mass," or a church service to celebrate God's anointed one.
But what about alternative name for Christmas? How did "Xmas" come about? Was it really done by baby-eating athiests to secularize a sacred Christian holiday? No.
While it may now be used by people who want to take Christ out of Christmas or who are too lazy to type out all nine letters of the word, Xmas has it's roots in antiquity. The initial letter of the Greek word Khrīstos (Χριστός) is chi (X). So "Xmas" does keep "Christ" in Christmas. And no, that's not some malarkey someone concocted to give legitimacy to "Xmas." In Middle English we see Χρ̄es masse where "Χρ̄" is an abbreviation for Χριστός.
But Christmas has been known by other names throughout history. The Anglo-Saxons typically referred to Christmas as "midwinter" for obvious reasons, though occasionally it was known as Nātiuiteð. The word Nātiuiteð comes from the Latin nātīvitās, which is where we English speakers get the word Nativity. Both the Old English Nātiuiteð and the Latin nātīvitās mean "birth." In Old English the word Gēola--or Yule to our 21st century eyes--referred to time in December and January. Over time it became nearly synonomous with the Christian celebration of Christmas. The word "Noel" or "Nowell" entered English towards the end of the 14th century from the Norman aristocracy. The Old French word noël or naël, words themselves derived from the Latin nātālis (diēs) "(day) of birth".
There you have it, a fun little lesson on the Etymology of Christmas and a few Christmas-related words. Hoping to have a few more articles of this kind this month. It's early in the season, but Merry Christmas!