As a child I learned about our local Native Americans, the Iroquois. However, recently I've heard the term "Iroquois" may be considered offensive because it means something rude in Algonquin. Would it be more correct then to refer not to the Iroquois but to the Haudenosaunee, as this is the league of six nations they created?
The exact etymology of "Iroquois" is debatable, and there are plenty of Iroquoian people who use it and related terms for various purposes. If you're talking about an individual person, it's best to go with their specific nation. Joseph Brant is Mohawk (or Kanien'kehá:ka if you're feeling particularly ambitious). Haudenosaunee is the accepted English variation for the name of the confederacy itself, based on the Mohawk name (Rotinonshonni). As such, it's reserved of usage for the political entity or its citizens as a whole. Joseph Brant was a defender of the Haudenosaunee, but he was not a Haudenosaunee.
Iroquois is used more generically, to refer to people culturally but often outside the context of the Haudenosaunee as a political entity. After the revolution, Joseph Brant led many Iroquois refugees to Ontario and helped found the Six Nations of Grand River (now home to the Iroquois Nationals lacrosse team) as one of the successors to the Haudenosaunee. In the derivative form "Iroquian" is extends to cover culturally and linguistically related peoples including the Wendat (Huron), the Chonnonton (Neutral), and the Cherokee.