For Cleveland: the legend is that the name Indians was in tribute to Louis Sockalexis, a “Native American” who played for the Cleveland Spiders. But this “is generally discredited given the discriminatory treatment of Native Americans in general, and Sockalexis in particular during that era...
“Defenders often claim there is an intention to honor Native Americans and that there are ways to do so while retaining their current representations. Opponents of Native American mascots make no distinction between respectful or disparaging usage, both being based upon stereotypes. “—Wikipedia
They could just make it “Hawks” as in the bird but chose to keep the full BlackHawks name.
“In 2010, sports columnist Damien Cox called on the franchise to retire the “racially insensitive” logo, saying that, “Clearly, no right-thinking person would name a team after an aboriginal figure these days any more than they would use Muslims or Africans or Chinese or any ethnic group to depict a specific sporting notion.”—Wikipedia