No, its really called "The Feast of The Incarnation" but thats to long to say
Christmas is two words, its actually Christs Mass....as in a Celebration of the Holy Communion to commemorate the Birth of Christ. All Feasts are Eucharistic Feasts, and traditionally they can be held to commemorate someone, thats what a Saint Day is all about.
So its The Mass which celebrates Christs Birth, the true word for the process is Incarnation (becoming part of creation)
If your interested, Easter isnt called Easter either, technically its The Feast of The Ressurection