The censuses give her name as being Chum Chees a Win Kah, which appears to be for Jąpcisawįga, from jąp, "lightning"; ci, "lodge"; sa, "to strike"; -wį-, a feminine gender infix; and -ga, a definite article suffix used in personal names. "Lightning Strikes the Lodge" is probably a Thunderbird Clan name.
In the 1930 Federal census, Luke Green is living with Johnny and Kate Mike, and is listed as Johnny's nephew. This would mean that Luke's mother was John Mike Jr.'s sister, so she should be the daughter of John Mike, Sr. So far she cannot be otherwise confirmed as his daughter in any census.