If you're primarily basing it out of Michigan then you might as well just use Michigan as the name. Alternatives might be Superior (which may have been the state name for the UP if it wasn't handed over to the state as a compromise deal to give up the Toledo Strip way back in Andrew Jackson's time; but even today there's a sort of cultural pride up north over the "Superior State" that sells flags at Wal-Mart).

You might also tag in a city name, which might be another easy solution; but it's Michigan so it hardly applies imo. Unlike New York State and New York City there's no real stand-out city to name this proposed nation off of. Detroit today is a shell of its former self having shed 60% of its population since the 1950's, and the other major cities - Lansing, Ann Arbor, Grand Rapids, Traverse City - are comparatively small when held against other major metro areas (Ann Arbor's a fun hipster and bohemian scene though, Grand Rapids for beer, and Traverse City for wine as an aside comment).

But to also add to what Vilage was going on with the Native American tangent they could identify themselves as Anishinaabeg, the plural of Anishinaabe which is the larger Indian ethnic group up here (comprising the Ojibwa and Potawatomi tribes among others). This might be a useful name to call one's self if you have desires to rope together the Great Lakes region since the Anishinaabe tribes covered the whole area and parts of Canada. They also all culturally have an immense attachment to water, but given the state is mostly Germans and Poles with Finns and Swedish people up north, I don't know if that applies so much; so it'd probably be used more as an echo of the back-then.

As an additional aside: I don't know if they'd take Chicago just to have access to Lake Michigan. They already have a city on that side with several naturally sheltered harbors: Traverse City. Mackinac Island would also serve as a premier launching or resting point at the boundary of Lake Michigan and Huron, it being off to the side of the Mackinaw Bridge and all. [url=https://en.wikipedia.org/wiki/Fort_Mackinac]Mackinac Island also comes with its own pre-built fort which'd be technologically relevant again[/url].