The name bestowed on you by your parents should be the one you legally have, but this has not always been the case for First Nations/Native American people once the Europeans took over and started all that legal stuff. Unable to pronounce, let alone write, native names, what had become the powers-that-be either gave them Christian names from the Bible or translated their native names into English. Such as turning the names of chiefs like Mahpiya Luta into Red Cloud, and Tasunka Witko into Crazy Horse. Tecumseh they could presumably manage, so he got to keep his. (‘Panther Crossing Across’ would have been a bit of a mouthful anyway.)
Even today, some native parents are having to fight to legally have their children’s names recorded in the proper manner.