Titles and names of groups can be confusing or misleading. One example: The Stockbridge-Munsee Indians. In spoken communication, people often don't realize that there is a hyphen between the words "Stockbridge," and "Munsee," so they make the reasonable, but incorrect assumption that the Stockbridges are a band of Munsees. Actually, of course, they are Mohicans, (or, arguably, they are amalgamated Algonkians). But who are the Munsee Indians?
A book that appears to be written for middle school students, The Indians of Lenapehoking (1985, Seton Hall University Museum) by Herbert C. Kraft and John T. Kraft addresses our question. The people who once lived in an area that included all of New Jersey, plus much of the land surrounding it, once called themselves the Lenape, or "the ordinary people." In the 1600's the English began calling them the Delaware Indians (page 2). (The Mohicans believed they were descendants of the Delawares and referred to them as their "grandfathers.")
According to Kraft and Kraft, "two related but distinct" groups of Indians made up the Delawares. Those living north of the Raritan River spoke a Munsee dialect, while those south of the Raritan spoke a Unami dialect (page 2).
(Map courtesy of the Wikimedia Commons)
The question of how the Stockbridge Mohicans became the "Stockbridge-Munsee Band of Mohican Indians" is too complex for me to get into now. Suffice it to say that the "Munsee" part doesn't refer to the Brotherton Indians, it refers to other Delawares that joined the Stockbridges later on.