According to the team:

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"The Chicago Blackhawks' name and logo symbolizes an important and historic person, Black Hawk of Illinois' Sac & Fox Nation, whose leadership and life has inspired generations of Native Americans, veterans and the public," the team said in a statement.

"We celebrate Black Hawk's legacy by offering ongoing reverent examples of Native American culture, traditions and contributions, providing a platform for genuine dialogue with local and national Native American groups. As the team's popularity grew over the past decade, so did that platform and our work with these important organizations."

The Chicago Blackhawks first joined the NHL in 1926, and it got its team name from owner Frederic McLaughlin, who was a commander during World War II serving under the 86th Infantry Division. It was nicknamed "Blackhawk Division" after Chief Black Hawk, according to the team's website.

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But there is also this:

The Chicago Blackhawks Foundation had previously partnered with the American Indian Center of Chicago (AIC) to educate the public about American Indians, but the AIC ended that agreement in 2019, citing the perpetuation of "harmful stereotypes."

https://www.cnn.com/2020/07/08/us/chicago-blackhawks-name-spt-trnd/index.html