I think it's similar to the "service taxi" I used to take on Cyprus occasionally from Limassol to Nicosia.
But (a) whether Cyprus is an English speaking country or not is debatable and (b) even if you count it as one, people in the US or UK would probably still not understand that name as it's not a familiar thing for them.
I know uber taxis from the USA. They don`t have a fixed route and pick up people on the go. It works with an app and is a pretty clever way to keep taxi drivers working when there is high demand instead of going home when they have met their daily goal because with uber the price goes up with the demand. So now you can get get a taxi in New York on a rainy day...pretty smart idea. I was wondering if a dolmuş worked the same way...