Hm. My answer didn't post, and I had to log in again.
I chose poorly, as the guardian says in the movie, but then I'd never heard of these before. I based my answer on "pastor" meaning shepherd, but that misled me.
I couldn't find anything on where the name comes from, but apparently they developed in Lebanese communities in central Mexico. They're apparently similar to döner kebabs. (When our younger son was studying in Berlin, he basically lived on döner kebabs, which are the most common form of fast food there.)