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
New Zealand
He goes by sliege. :)
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.