Although it probably doesn´t help to find out his name, I think I have found another portrait of this man, who likely is a Hunkpapa man, at least it was said so at an auction site:
here´s the second portrait:
I think he is Medicine, who was a performer in "Buffalo Bill" Cody´s Wild West Show. As you see below, he was also labeled 'Medicine Man' and 'Medicine Horse'. Medicine Horse was one of the 'chiefs' in the contingent of Lakota performers on the tours around 1889/1890.
George Spencer photographed Medicine in 1891 in Chicago:
Here he is with another Wild West Show performer:
Medicine Horse & Plenty Horse [who is rather Painted Horse] (colored photo)