I'm a fan of names that have some history behind them. Per Wikipedia, these are all the former Cleveland baseball teams:
Cleveland Forest Citys, National Association (1871–1872)
Cleveland Spiders, National League (1879–1884, 1889–1899)
Cleveland Blues, American Association (1887–1888)
Cleveland Infants, Players' League (1890)
Cleveland Bearcats, American Association (1914)
Cleveland Spiders, American Association (1915)
Cleveland Tate Stars, Negro National League (1922)
Cleveland Browns, Negro National League (1924)
Cleveland Elites, Negro National League (1926)
Cleveland Hornets, Negro National League (1927)
Cleveland Tigers, Negro National League (1928)
Cleveland Cubs, Negro National League (1931)
Cleveland Stars, East-West League (1932)
Cleveland Giants, Negro National League (1933)
Cleveland Red Sox, Negro National League (1934)
Cleveland Bears, Negro American League (1939–1940)
Cleveland Buckeyes, Negro American League (1943–1948, 1950)
I think Spiders would be cool.