Are there any native American names that have this spelling taishka?
No, that is not a native American name. It is a name used in Russia (spelled using the Cyrillic alphabet) and also a name from parts of India and Shri Lanka (Ceylon).
Idaho . . . no. Bonner's Ferry Sandpoint Coeur d'Alene Plummer Moscow Lewiston Grangeville Pierce New Home Boise Caldwell Nampa Marsing Weiser Buhl American Falls Idaho Falls Gooding Riggs None are native American names. Even the name, "Idaho" is not an American native word, but was invented by early entrepreneurs and politicians. If you want American native names, check out New Jersey.
That would be Kelli. All of the Native American groups have their own language and dialects. Proper names to them would be the "english" word as those groups didn't use "proper" names as we do today. Native American names were earned by deeds or given based on other actions/habits. Name examples would be Crazy Horse, Red Cloud, Sacajawea..etc.
Bozho (hello) It could be, most Native Americans have normal names, you would not want someone calling you two birds over the earth in class. Native American parents usually name their children a normal American name and then have a Native American name. David, member of The Pokagon Band of Potawatomi
There are hundreds of male Native American names and all of them have unique meanings. Sometimes these names relate to Native American culture such as Hiamovi, a Cheyenne name meaning "high chief". Other names simply carry meanings related to everyday things. Some examples of such names are Avonaco, a Cheyenne name which means "lean bear" and Makkapitew, an Algonquin name meaning "he has large teeth".