I like "people" names for dogs. Never cared for names like, "patches" "spot" "fluffy" etc.
If you want to carry on the Christmas theme, you could name him "Nic" (for St. Nicholas) or "Rudolph" or "Rudy" for short-- for the rednose raindeer.
For a small dog like that, I like, "Bobby" "Cleo" or "Jess." Or if you want something more formal, "Miles" "Zach" or "Wallace."
Here is a website with more than 2000 dog names:
http://petrix.com/dognames/