What is the name of this drink and is there a substitute for the pineapple?
From the description of how this beverage is made, it is not fermented.  Four hours, at refrigerator temperature, and without any inoculation from an active bacterial culture simply will not cause any significant amount of fermentation.

Instead, what is happening is that the enzyme bromelin and acid present in pineapple is curdling the milk proteins, lending it a thicker texture.  This is very analogous to some types of cheese making.

I was not able to determine a name for this beverage.