As I told you before, and I am sure others, too: Christmas has nothing to do with Christians, especially today. Anyway, Jesus was born around August or so (if he existed) so Jesus day should be then. My sister-in-law is a strong atheist, she celebrates because even she agrees it has nothing to with Christianity.
I recently bought a 2-film Christmas collection of It's a Wonderful Life which only mentions angels. Doesn't mention Biblegod or Jesus, or anything. What Christianity is in that movie? And the other film White Christmas. Where is Jesus and Biblegod in that film? "Lord" was mentioned in a song but past that: no where else. See, even back then Christmas wasn't about Christianity--when has it ever?
I will be celebrating xmas EXACTLY the way I did before I "deconverted." Which is to say, I go bananas decorating til it looks like "the house that threw up xmas" - put up a HUGE tree, watch tons of xmas movies, listen to cheesy xmas music, bake cookies for the neighbors with the kids (a yearly tradition for a decade now), buy dumb but fun presents and in general just enjoy the crazy holiday atmosphere - I LOVE it.
I see no reason to rename it or try to change it. It's not necessary.