Most English speakers are used to the word Noel meaning Christmas. The o is long and the second syllable gets the volume stress.
The word Noel, sometimes with different spellings, is a given name as well.
According to Merriam-Webster, the origin of noel is:
French noël Christmas, carol, from Old French Nael (Deu), Noel Christmas, from Latin natalis birthday, from natalis natal
The English word for the original gathering or a display of the holy family in the manger at the time of Jesus the Christ's birth is nativity. It can also refer more generally to the process or circumstances of being born.
Again from Merriam Webster, the origin of nativity is:
Middle English nativite, from Anglo-French nativité, from Medieval Latin nativitat-, nativitas, from Late Latin, birth, from Latin nativus.
Other references tie nativus and natalis to nasci (to be born).
The Irish (Gaeilge) word for Christmas is Nollaig.
Interestingly, Nollaig can also be a person's given name as well.
And to make life interesting, Nollaig is also the Irish name of the final month of the year or December in English.
Nollaig has cousins in other Celtic tongues such as:
Nollaig - Scottish Gaelic
Nollik - Manx
Nadolig - Welsh
Nedelek - Breton
Nadelek - Cornish
The resemblance of Nollaig to Noel and nativity is obvious in the history of the words.
In Old Irish the word for Nollaig was "Notlaic" and this compares to the Latin "natalicia" (for the day of birth), from the verb "(g)nasci" (to be born).
Some say the precursor language to both the Latin and the Celtic tongues was Indo-European and the word for birth in Indo-European was *gen- (to give birth).
Upon first inspection, there seems to be a large difference between words starting with g and words starting with n. However, an author named Joshua Wachuta has put it this way:
The letters gn often simply make the n sound, and this has given rise to cognates that have dropped the g entirely. Consider the word natal, an adjective meaning "of or relating to birth." It shares an obvious relationship to gen- in meaning, but at first glance it bears little resemblance in sound or spelling. Children, however, don't always look like their grandparents. Sometimes it's more useful to compare cousins, like natal and genital. Suddenly the resemblance becomes apparent. The new root, stripped of the g, has given rise to other similar words like nascent, native, and nativity.And now we can add: words like Noel and Nollaig came from the Indo European *gen-.
Whether you say “Happy Noel to you,” "Feliz Navidad," or “Nollaig shona duit,” we wish you the best in this time of birth and renewal!