Three suggestions is no particular order:
1. The Cougers. A fierce, predatory, American cat. The name is not taken by any pro teams and it's alliterative and sounds good rolling off the tongue, IMO. Same family as Lions, Tigers.
Alternative that is more interesting: The Lynx. However, some fans may be reminded of golf courses.
2. The Guardians. I had no idea where this came from until I googled it. This is probably the best historical name, IMO. The Guardian statues have been gracing the city since 1932. They're art deco and pretty cool looking, IMO. The name would also be unique. How many pro sports nicknames refer to works of art? In fact, the Cavaliers have already used the image of a Guardian on a new banner celebrating "The Land".
The bridge’s guardians are icons for the city, imagined nearly a century ago, when Cleveland was the fifth largest city.
www.ideastream.org
3. The Thunderbolts. I'm going with a force of nature nickname here, like the Oklahoma City Thunder, the Seattle Storm (WBA), and the Miami Hurricanes. The thunderbolt was a weapon of the gods.
"Zeus's Lightning Bolt (a.k.a. Thunderbolt, a.k.a. Master bolt) is the signature weapon and symbol of power for the Olympian god of thunder; Zeus. It is said to be the most powerful and feared weapon on Earth and in the Heavens."
No connection to Cleveland, but I think it would be a really cool nickname. It could be shortened to Bolts in headlines and for our blogging purposes.
Please, no insects, nuts, or common non-predatory birds. Bluebirds? Why not Titmouses?
Also, no names of former players. The Cleveland Naps? Why not the Cleveland Fellers, the Cleveland Lemons, or the Cleveland Belles? The latter might appeal to the gay and transgender fans.
I can't find much wrong with the Commodores, but I like my three suggestions better.