Only those cheese that have been made using a Vegetable or Microbial coagulant (instead of Rennet, which is derived from animals.) I was previously of the assumption that the “enzymes” in the ingredient list of any cheese would naturally mean vegetable/microbial enzymes. I assumed wrong. It only means that it used enzymes that could be either vegetable, microbial or animal. Mostly Vegetarian cheese would label theirs as that or use the term “vegetable rennet” in their ingredients list.
I have listed the nomenclature generally used by such cheeses.
Medium Cheddar Cheese has the term "No Animal rennet" mentioned in the ingredients section.
Monterey Jack Cheese made with "Non-Animal Enzyme"
My all time favorite Cheese - fresh Mozzarella here uses "Vegetable Rennet"
Here is another brand for Monterey Jack Cheese that mentions "Vegetable Enzymes" in its list
If using enzymes from a vegetarian source, it is indeed mentioned likewise. Like here - "Microbial Enzymes".
Apart from that, some brands (mostly available at Whole Foods Market) advertise the fact right in your face. Like this Parmesan that I get from my local Whole Foods Market :)
Some companies will specifically list `rennet' or `rennin' while others might just say `enzymes.' Other terms to look out for include `chymosin' and `rennase.' For those that list `enzymes,'these are most likely animal enzymes. Even some cottage cheese and sour cream products contain rennet. If a company is using microbial enzymes, it will probably state specifically `vegetable enzymes' or `vegetable rennet.'
Here is a website, that might be useful to you, where there is a comprehensive list of Cheese brands that are vegetarian. Browse by Type or Browse by Brand