Searching Blackfeet Rolls for Ancestor and Name Question

Hey, all!

  For years I was searching for my great-grandmother on my father's side as a member of the Cherokee tribe. My father recently told me that it was actually the. Blackfeet, tribe that she a part of, which doesn't make sense because of the geographical location of the tribe being Canada and the upper plains states and where my great-grandmother ended up, in Lawrence, KS. I have been on Ancestry.com (I found a few close names but the dates aren't right), MyHeritage.com, FamilySearch.com, and I have scoured the Archive.gov websites to find anything useful but I cannot find her name. I can find her last name, Horton, in the rolls of many different tribes but not the Blackfeet around the time when she would have been born, between 1895 and 1900 (I'm guess-timating). Where else can I search?

Also, how did the naming work way back when? When a Native American took their English names from the government, was there any history or persons/people associated with the name? The name I found most closely resembling who I believe to be my great-grandmother, has a line before her, such as a father. mother, grandfather/mother....could someone please explain this to me or tell me where I can go to research this information? I've always wondered.

Thanks in advance!