The "gift bringer" as u say in the UK is father christmass a.k.a jolly saint nick and santa clause
Julemanden is the gift bringer in Denmark
santa
Babushka
The gift bring of Africa is Christian noel
Santa
santa
ಸಾ೦ಟಾ ಕ್ಲಾಸ್
Papai Noel
they call him Christ Child
In Chile, they call the person who brings gifts at Christmas Viejito Pascuero. The words translate to mean Old Man Christmas, who is the gift bringer.
The Hawaiian gift bringer is known as the Menehune, who are believed to be mischievous little people in Hawaiian folklore. They are said to bring gifts and help with chores during the night.
New Zealand