Question

I do not know his father's name

Comments

Looks like this is your guy:

WWI draft registration gives his mother's name as Lena and his home as Etowah, Alabama.   "United States World War I Draft Registration Cards, 1917-1918", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K3PF-C7T : 23 August 2019), William Clifford Barnes, 1917-1918.

Here is Will in Etowah with mother Lena and father Charles in the 1910 census:  "United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MKQF-BHJ : accessed 11 September 2020), William Barnes in household of Chas V Barnes, Gadsden, Etowah, Alabama, United States; citing enumeration district (ED) ED 56, sheet 2B, family 39, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 13; FHL microfilm 1,374,026.

Answer 1

Welcome to G2G, Rita.

William Barnes was the son of Charles and Lena Missouri Barnes.

See the original document of his WWI Draft Reg. Card. The listed nearest relative is his mother Lena Missouri Barnes.

Name: William Clifford Barnes
Event Type: Draft Registration
Event Date: 1917-1918
Event Place: Etowah, Alabama, United States
Gender: Male
Birth Date: 10 Apr 1899
Birthplace: , , United States
Citizenship Place: United States
Affiliate Publication Number: M1509
GS Film Number: 1509383
Digital Folder Number: 005146831
Image Number: 00795
Citing this Record
"United States World War I Draft Registration Cards, 1917-1918", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K3PF-C7T : 23 August 2019), William Clifford Barnes, 1917-1918.

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William and his parents in the 1900 Census:

Name: William E Barnes (He is listed William C. See the original document)
Event Type: Census
Event Date: 1900
Event Year: 1900
Event Place: Anniston city Ward 1 (all that west of Noble street), Calhoun, Alabama, United States
Event Place (Original): ED 42 Anniston city Ward 1 (all that west of Noble street), Calhoun, Alabama, United States
Gender: Male
Age: 1
Marital Status: Single
Race: White
Race (Original): W
Birth Date: Apr 1899
Birthplace: Alabama

Household	Role	Sex	Age	Birthplace
Charley V Barnes	Head	M	27	Alabama
Lena M Barnes	Wife	F	23	Alabama
William E Barnes	Son	M	1	Alabama
Margaret Barnes	Daughter	F	4	Alabama
Newton Barnes	Brother	M	25	Georgia

Citing this Record
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M9ZB-CJ9 : accessed 11 September 2020), William E Barnes in household of Charley V Barnes, Anniston city Ward 1 (all that west of Noble street), Calhoun, Alabama, United States; citing enumeration district (ED) 42, sheet 10B, family 208, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,240,005.

Answer 2

Per his World War I draft card (behind paywall at ancestry.com) his mother's name was Lena Missouri Barnes, and they lived in Etowah Co., AL. As a result, he can be identified in the 1910 census as the William Barnes, age 11, in the household of Chas V Barnes and Lena M Barnes in Etowah County, AL - in other words, his father is Chas V Barnes. According to information at familysearch.org, Charles V. Barnes was born 30 Oct 1873 in Rome, GA, and died 12 Apr 1935 in Birmingham, AL.