Cleveland Rocks is the really cheesy joke/suggestion.
I've also seen The Cleveland Baseball Club suggested as an old-school (almost soccer-like) approach, rather than a temporary thing.
Another way to go would be to figure out something that actually honors Native American history in the region, though said history is mostly dishonorable. Even "Cuyahoga" is thought to be a bastardized word from no actual nearby culture.
The way things work these days it will probably involve a branding agency and a (non-binding) fan poll.