What is the version of Santa Claus in your country/region?
In Russia, he's called Ded Moroz. Unlike Santa, he wears blue, doesn't ride a sleigh, nor does he abuse his workers, but uses magic to deliver the presents instead. He has a granddaughter named Snegurochka, who always comes with him to kids' celebrations. Just as the new year starts, he's ready to put the presents under the fur tree.
In Norway we call him julenissen, or just nissen. Today he's very similar to the Santa Claus as the English-speaking world knows him, but the name hints at him being a very different character back in the day.
Jul was the name of a month in the old Germanic calendar, a month where the end of the year was celebrated. I guess the church though it was easier to co-opt the old pagan celebration than to attempt to outlaw and replace it.
Nisse is a mythological creature that translates to something like gnome or goblin. Often, especially in older artwork, julenissen is depicted as a short man with a pointy hat.
The modern julenissen delivers presents on Christmas Eve (which is also when we open the presents). We leave him a plate of rice pudding to thank him; in the barn if your family has one, otherwise outside the door of your house/apartment. His reindeer are unnamed.