From the 13th century onwards, both boys and girls, born at Christmastime in Britain, were given the name Christmas, either as a first or a middle name. This practice was used right up to the mid 20th century, when alternate Christmas names, such as Carol and Noel were favoured instead.
The French word for Christmas is Noël, which has also been used as both a feminine and masculine name since the Middle Ages. Now it is generally considered more of a masculine name (most likely due to the fame of Noël Coward), while Noelle, Noèle, Noelia, Noella and Noelene are used as feminine forms.
The Latin name for Christmas Day is natale domini, literally "birthday of the Lord." From this term came the Late Roman names Natalius and Natalia.
Natalius later became rendered to Natale in Italian and Natalio in Spanish, but it was the feminine Natalia that has made a particular mark, most likely thanks to having been borne by St Natalia, wife of St Adrian of Nicomedia. She is particularly revered by the Eastern Orthodox Church, which is why the name has been so popular in Russia and Greece.
Natalia has many international derivatives including Natalie, Nathalie (French, German), Nathalia (Portuguese), Nataliya, Natalya (Russian) and Natalija (Serbian).
Natasha, from Russia, is perhaps the most famous of all Natalia's diminutive forms, but there is also: Nata, Natalka and Tasha.
I wish you all a very merry Christmas and a happy and healthy New Year.