The Brush St. depot was indeed one of Detroit's earliest train stations. But that location was for the predecessors of the Grand Trunk [[Detroit & Pontiac, Detroit & Milwaukee, Great Western), not Michigan Central. That depot's 19th Century replacement was in use for Grand Trunk commuter trains until the small station was torn down for the construction of the Renaissance Center in the mid-70s. Even after that, the platforms remained, and trains still ran there, until commuter train service was ended in 1984.
1880s maps show the nearest large hotel as the Wabash. But since it was not a Michigan Central station there wouldn't be anything named after that line there anyway.
Brush St. Depot:
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