|Really, it's no one's birthday: just created to fit the calendar, for there is no particular record - or, for simplicities sake, ask a member of the Greek Orthodox faith the calendar date of your festival.
And that's what the December celebration was: the festival of Janus, the two-faced god of coming-and-going (amongst other things). Hence, the new year is this time of year.
The gifts, yule-logs, tree decorations? They're all from what you'd call pagan customs and rituals. The christian church adopted a tremendous amount of this stuff, decorated it to suit there needs, and went on celebrating them. It was a good way to get converts.
Other examples (sorry to burst more of your bubbles): easter bunnies and eggs? All are from the fertility festivities that were part of the coming of spring.
Before you reply, however, consider the following: you faith should secured by its philosophical teachings and values, and not the decorative trappings. If the above notes really do anything to harm the worthwhile aspects of your beliefs, then you should have a long and hard think. There are, indeed, christian sects who disavow all of the seasonal trappings in the practice of their faith: does that make them less christian?
Try Malachi 1:11 - and I suggest you try several translations, for some tend to distort this message, from a recognized prophet, which is that all believers, in all faiths, are acceptable.
'For, from the rising of the sun to its going in, Great [is] My name among nations, And in every place incense is brought nigh to My name, and a pure offering, For great [is] My name among nations'
"As far as we know, our computer has never had an undetected error." - Weisert