I think the original plan was to make "The Madison" a Yellowstone spinoff, but I read an article today that explained although it's in the Taylor Sheridan universe, it's not really a spinoff from Yellowstone. It's a standalone show. The show is a modern-day story about the Clyburn family as they settle down in the Madison River Valley after making the move to Montana from New York City. A press release described it as "a profound love story channeled through a deeply personal family drama about resilience and transformation".
I think "The Madison" sounds like a swanky hotel.