Jack - this is a Scots surname, meaning John (diminutive), or James, via the French Jacques. A Native American might just have taken the name by which her father was known in English. Same process as in Scotland, but occurring later. With the Lakota it's also possible that the name started out as Jacques, as, I believe, some of that nation were given names by French missionary priests.
Towns - English and Scottish, someone whose home was a farm, the old meaning of town.