In the USA, parigiana is practically synonymous with italian food. We have this powdered cheese product that comes in a plastic can that sort of replicates the msg flavor but has a gritty feel due to an anti-caking agent we add to the powder.

But fancy italian cheeses are widely available as well, and many grocery stores carry proper parmesan, romano, provolone, pecorino, gorgonzola, asiago, mascarpone, ricotta, and of course mozzarella. Ironically, it's the areas where dairy farming is most popular where you find fewer international options, but that's just because there will be 20 local variations of cheddar.