As I work my way thorough the draft registrations in Kansas, there are several registrants who only have Native names, meaning names in the Native language and no English names. For example, there is a John Nag-Mo, except he signs his name only Nag-Mo and then by an X, no John. His next of kin is M-sco-ta-quah. They live in Brown Co., Kansas, so most likely one of the Potawatomi tribe. There are several more people with names like this, with or without an “English” first name.
One of the most interesting aspects of this group of people still utilizing purely Native names as late as 1918 or so is that none of these people knew their birth date. They all knew their birth year, but not the month or day. One had a month with a question mark. The registrar did not simply leave that field blank, but wrote in that the person didn’t know. I think we can deduce from this that people still living a culturally Native lifestyle didn’t record or care about their actual birthdate, but they did care about the year, or how old they were.
It appears from this information that there may have been a cluster of people in that timeframe on the Potawatomi Reservation that were much more conservative and much less acculturated than the majority of Native people in the first quarter of the 20th century. It’s unusual to find tribes that lived among Europeans that did not at least adopt English first names. Perhaps some were simply assigned to them. Maybe John hadn’t been John very long, and maybe he wasn’t John after he left the draft office.
I turned to the 1920 census to see what that shows us. Indeed, we do find John Nag-mo, but he is mis-indexed at Ancestry. He is age 46, and interestingly enough, listed as white. His wife, Lizzie, 42, is listed as Indian as is their 5 year old child who carries only a Native name.
Native Heritage Project 
I have been researching the Eastern Cherokee Payroll applications (commonly called Miller Roll) and have found that Cherokees of that era who were living a traditional lifestyle, did not usually know their date or year of birth or even their age. When asked, they would guess or give a response that related their birth to an historic event, such as “before the war (Civil)” or “A year before the payment.” How long this persisted among the traditional Cherokees is unknown, as there are no records giving as clear an indication of what they did not know as the Miller Roll. This is in stark contrast to the culture of traditional Cherokees today who make a big deal out birthdays, particularly those of elderly matriarchs, hosting hog or fish fries and/or gospel singings to mark the event.