Hi, in my experience:
In Spain, I would call it Kebab (mostly beef or chicken, unfortunately lamb is rare)
In Australia, where I lived for years till recently, it's upon the place, in greek restaurants you have Slouvaki (lamb, beef, sometimes chicken), gyros (pork) but also durum or shawarma (lamb, beef, chicken) in street food places with middle-east fashion. In Australia, kebab is what we call in Spain "pinchos morunos", roughly.
I also know that in mexico tacos al pastor are done in this way (Lebanese inmigrants make it popular in that country) [known from Mexicans BTW]
Hope it helps
cheers