Just thinking out loud here, but the words Michigan and Michoacan are way too similar to each other for them not to have shared indigenous roots

Oh shit, it's true! Michigan is based on the Chippewa word "meicigama," meaning "great water." Michoacán derives from Náhuatl terms michin (fish) and hua (those who have) and can (place), which roughly translates to "place of the fisherman."

There's also this neat documentary about Valeriano & Martina Fraga’s migration story from Michoacan to Michigan in 1919. https://www.dia.org/events/michoac%C3%A1n-michigan

I can't find anything definitive tieing both words right now, but there are indigenous people who take both words and their similarities as a sign that indigenous nations share a deep history across present-day borders https://www.youtube.com/watch?time_continue=3&v=iXcwKeWp1LA&feature=emb_logo