Hi! I’m a PhD Candidate writing a dissertation about the Native American conflict during the Civil War (specifically Bear River Massacre and Owen Valley Expedition).

Short answer, historians typically favor Iroquois over Haudenosaunee, although the latter is sometimes mentioned as an alternative title. There’s a few reasons why, mainly readers are familiar with “Iroquois.” However, if you are the writer, it’s up to you to choose and explain your preferred naming conventions.

Extra stuff:

One has to be careful to define the terms they use to name various Native societies. In the case of “Iroquois,” Daniel K Richter (in his excellent history of the Iroquois League) uses the term “Iroquois” to describe a related or allied group of tribes, while using more precise names—Mohawks, Oneidas, Onondagas, Cayugas, Senecas, Tuscaroras—to describe individual tribes.

Historians (like Brigham Madsen) also identify specific bands by name—Northwestern Shoshone, Eastern Shoshone, Gosiute, etc—while using “Shoshone” as a generic or collective title. Madsen also used “Shoshoni” instead of “Shoshone” because he believed it was the more “authentic” spelling. In my work I opt for “Shoshone” because the band I’m writing about employs that spelling.

Ultimately, it’s up to the author to chose their naming conventions and explain them in an early footnote or introduction.