I'm looking to create a pet on Christmas and with a name that belongs to the holiday. Everything I've searched for is taken. Help is greatly appreciated!

Here's a few words I scraped up that are free!

Carols Giftwrap Giving (“The Season of Giving”) Greetings (“Season’s Greetings”) Manger Poinsettias Snowmen Unwrap Workshop (“Santa’s Workshop”)

I found some available two-word names as well:

Happy Holidays Jingle Bells Merry Christmas Silent Night

And lastly, here’s some more wintery words!

Frostbitten Snowbound Snowed Snows Slushy Thaw

Like you said, unfortunately there's a lot of stuff already taken but I hope it helps a little bit! ; u;