On the 1900 Harpersville, Shelby, AL Census , it looks like Rosetta had another son other than Dock. There is a Nelson Dunaway (indexed as Donaway), grandson, b. AL Feb 1900.
1910 jefferson Co. AL, Dock is living with his Dunaway grandparents and listed as a son.
Married: 7 May 1914, St. Clair Co. AL
Source: AL County Marriage Records 1805-1967
Must not have lasted long.
Dock Field Dunaway
Born: 5 Sept 1900 [interesting different date]
1918 Res: Cropwell, St. Clair Co. AL
Occ: Self-employed farmer, Cropwell
Nearest Relative: Mrs. Rosetta Joiner, mother, Cropwell
Source: U. S. World War I Draft Registration Cards 1917-18
1920 Easonville, St. Clair, AL
Dock is living with his grandmother, mother (Rosetta Joiner) and half siblings. He's listed as a nephew.
Dock Bright, b. AL, 31, farm laborer
Etta, b. AL, 21
Floyd, b. AL, 3
Eva J., b. AL, 1
Clem Dunaway, uncle, b. AL, 45, farm laborer
Howard S. Dunaway, cousin, b. AL, 15, farm lab
1940 Jefferson Co. AL
Dock Bryant, b. AL, 43, farmer, education=none
Alta, b. AL, 28, educ=3rd grade
Floyd, b. AL, 13
Eva Jane, b. AL, 11
Mary, b. AL, 9
Dock, b. AL, 7
Lou Ella, b. AL, 5
Clyde, b. AL, 2
Claud, b. AL, 7/12ths
I don't know if he would have officially changed his surname to Bryant or not. You'll find St. Clair County court records at the Alabama Archives and History, www.archives.state.al.us/referenc/pcounty
I looked for an Ought Bryant in Shelby County around 1900 but didn't find him. I can only assume that Dock found out the name of his father and decided to use his surname. I don't understand why his mother and grandparents neglected his education.
A DNA test might help prove who his biological father was. There are lots of articles about that on the Internet and books in the public libraries. Successful Searching!