They're barely in, but some suggestions for Brazil (and for the yet to be included argentinians)
Brazil, if:
*Tyranny, dynasticism or theocracy, regardless of everything else: Empire of Brazil (Kingdom of Brazil was a very short-lived name)
*Totalitarianism or representation or universal suffrage or egalitarianism: Federative Republic of Brazil (odd, yes. The dictatorship adopted the name, and it was kept by the democratic government. So it should represent BOTH a non-populist military dictatorship and a mature democracy)
*Vassalized to portugal: Principality of Brazil
*Default name: United States of Brazil
Argentina, if vassalized to Brazil: Transplatine province