The United States of America is called "America" in English. The landmass that includes both America and Brazil is usually called the Americas, the New World, or the western hemisphere.
I know that some South Americans like to make the point that the USA doesn't encompass all of "America" or "the Americas", (North and South). I understand the point to a certain extent, but what's done is done. We named this country America more than 200 years ago, and we have no other name for it. I'm not always going to say "United States of America", just like a Brazilian isn't always going to say "Federative Republic of Brazil". The name is what it is.
Historically, there wasn't a good widespread name for the region that would later become the USA, and the Thirteen Colonies called themselves America partly because they were the first independent state in the Americas and were, at least theoretically, building themselves on a philosophy of New World-based independence from European colonialism (a philosophy that later culminated in the independence of other states in Latin America).
In short, we called ourselves America because we were the only significant nation-state really based in "America" at that time - Brazil was Portugal and Mexico was Spain at that point. There's a certain arrogance to that name, perhaps, an arrogance which might offend other "American" countries. But again, we have no other name for it. I am NOT always going to say "United States of America." Sometimes I'm just going to say "America", and Canadians and Brazilians and whoever else will just have to deal with it.