Gustave John was, by family legend, captured by Indians and later adopted by the Pauly family. This is historically quite possible, as there was a major Indian uprising in Minnesota in the summer of 1862 when Gustave John was 7. Additionally, he was absent from the John and Anna Pauly family in the 1860 census when he would have been 5 years old. He was with them in the 1870 Census.
A great-granddaughter recalls that her father said that John Gustave's family was in a wagon train when captured. She recalls her father finding the name Owen in a log.
A great-grandson recalls his father telling the story of the capture and adoption, and saying the original name, which sounded Irish or Scotch.
There does not seem to be any official record of this adoption, which might favor that it was a family adoption.
See also a news item on this website.
Note
Captured by the Indians: reminiscences of pioneer life in Minnesota. By Minnie Buce Carrigan.
I have these census records which may tell you a time of the adoption: 1857, Township #116, Carver, MN: John and Anna Pauli; 1860, Chanhassen, Carver, MN: John and Anna Paulie and a farm laborer by the name of William Baker; 1865, Minneapolis, Hennepin, MN: John Pauley, Anna and Gustiff (no ages were given in 1865 census). So he must have been adopted between 1860 and 1865 but it's not clear if it was in Minneapolis or Chanhassen.