the most popular cheese, far ahead of anything else, is mozarella... it is not high quality as actual italian ones though (it is way less "fibrous").
then we have Prato (it means "Plate" as in dinner plate... or dinner dish...), that has the exact same recipe as Danbo, but is made with brazillian milk, and seemly tastes very differently (I dunno, since I never ate Danbo).
then we have a purely local invention called Minas, named after the state of Minas Gerais, despite being a São Paulo invention... (go figure...), that one is hard to describe, since it refers to 4 different cheeses (or the same cheese with 4 slightly variations in the process to make them, but with end results drastically different).
Then other italian cheeses are popular here, maybe because the large italian community here, and how much Brazillians also love pizza, so here almost every supermarket offers Provolone, Parmesan and Gorgonzola.
In urban areas you can find frequently "Steppe" cheese, it is a russian cheese it seems, it is expensive (double the price of "Prato") but not much as local clones of french/swiss cheese (Steppe is half of the price of local clones of Emmental, Gruyere, etc...)
cheddar cheese is sold a bit, but most people consider it low quality crap, the biggest seller of cheddar cheese don't even bother in selling actual cheddar, and instead sell a clone that tastes mostly the same, for very little... people still prefer to buy more expensive mozarella instead.