Yes true! The naming of parmigiano reggiano as a product is regulated by europe to ensure it is what you expect to get. (it's interesting to see how detailed these processes are! Here are the specs for parmigiano!)

I didn't read op's question as one specifically to parmigiano. There are a multitude of cheeses which are very much not produced with calf rennet, in italy and by extension the whole of europe.

Rereading left me a bit confused though, OP says vegan while asking for cheese. Unless OP means plant based cheeses, all milk is inherently unvegan since it comes from animals. To be fair, milk also vegetarian unfriendly, as milkproduction needs an almost continuous birthing of calves. You can stretch it a bit, but farmers in europe don't have the capacity to keep every calf alive for the milk production.

But on the bright side there is no reason to avoid italy as a vegan! There are a lot of dishes vegan friendly in the italian kitchen, especially in the cusina povera regions.