On the 1880 Cherokee Census, infant Will Rogers is listed as "Col. W.P. Rogers". Col. William Penn Adair was referred to as "Colonel Adair" for the rest of his life so it makes sense the family might have called little Will Rogers "Colonel". On the 1896 roll (pre-Dawes census) he is listed as Wm. P. Rogers and on the Dawes Roll he is recorded as William P. Rogers. There were no official birth certificates so his name was whatever was first officially recorded, which I suppose would be the Dawes Roll, but I don't think there was anything that kept a person from changing their name as they chose since there were no drivers licenses, social security cards, etc.