While I might agree with the Indians, Redskins, and others with those generic names being dropped, I don't see and issue with Chief's, Warriors, Braves, etc. They're names that are on a more spectacular platform, we're Warriors! Maybe they change a look and feel of the logo, but that's about it.
In theory, they play on the Cuyahoga River, Cleveland Cuyahoga's.
Seriously, here are the past team names.
Cleveland Indians (1915–present)
Cleveland Naps (1903–1914)
Cleveland Broncos (1902)
Cleveland Bluebirds (1901)
Cleveland Lake Shores (1900)
Grand Rapids Rustlers (1894–1899)
I'm thinking, go OG, Cleveland Rustlers.