Santa Claus or...

In the United States and Canada, his name is Santa Claus. He flies through the sky in a sleigh pulled by eight reindeer. 

In England his name is Father Christmas. He looks much like Santa Claus, but he has a longer coat and a longer beard.

In France, he's known as Pere Noel. He is also called Pere Noel in Canada. 

In Germany, children get presents from Christkind, the Christ Child on the 24th of December. 

In Poland, Santa "Swiety Mikolaj" (Saint Nicholas) - he visits children on December 6th and he brings presents, mostly sweets, which he leaves in children's clean shoes. 

In Costa Rica, Colombia, and parts of Mexico, the gift bringer is El Nino Jesus, "the infant Jesus." 

In Puerto Rico, children receive gifts from the Three Kings on January 6th. Each child puts grass under their bed for the camels and in the morning the grass is replaced with gifts. 

In Finland, he is called Joulupukki and his home is in Lapland in the north part of Finland

In Spain the children the night of January 5th put their shoes under the Christmas tree and have presents from the Three Kings (Los Reyes Magos: Melchor, Gaspar and Baltasar). Santa Claus is called Papa Noel and there are children who have presents both days on December 25th (from Papa Noel) and on January 6th (from the Three Kings). 

In Russia, he is called Grandfather Frost or Ded Moroz

In Italy, he is called Babbo Natale. Also, they recieve their presents on January 6th from the gift bringer an old lady called Befana. 

In China, he is called Shengdan Laoren. 

In Denmark they call him, Julemand. 

In Slovenia they call him, Bozicek. 

In Austria, children get presents from Christkindl, the Christ Child on the 24th of December. 

In Greece, Santa Claus is called "Aghios Vassilis" and he comes on the night of 31st December leaving the presents under the tree for the children to find them on New Year's Day. 

The name for Santa in Yugoslavia is Deda Mraz. 

In Croatia, he is called Bozicnjak. 

In Bulgaria they call him Diado Coleda.