Appears to be a Nickname:

William H Blair

William H Blair
Waters Family Tree
Birth: 7 Aug 1844 - Pike, United States
Marriage: 1868 - Alabama, United States
Death: 11 Aug 1911 - Brewton, Escambia, Alabama, United States
Parents: William Henry Blair Sr, Elizabeth Harrison
Spouse: Sarah Annie Cooper

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William Henry Blair Jr
Find A Grave Index, 1600s-Current

Name: Pvt William Henry Blair Jr
Birth Date: 7 Aug 1844
Death Date: 11 Aug 1911
Death Place: Escambia County, Alabama, USA
Cemetery: Cooper Cemetery
Burial or Cremation Place: Appleton, Escambia County, Alabama, USA
Has Bio?: N

Find A Grave Memorial # 5344303

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BLAIR, William Holly (Private, Company “F” 36th Alabama Infantry Regiment) Born: 1817, South Carolina - Died: February 4, 1864, Rock Island, Illinois and buried: Rock Island National Cemetery, Rock Island, Illinois Grave #364. Captured at Missionary Ridge, Tennessee on November 25, 1863, William Holly Blair, Sr. died of pneumonia. Source: Keith Janes

BLAIR, William Holly Jr (Private, Company “F” 36th Alabama Infantry Regiment) Born: August 7, 1844, Troy, Pike County, Alabama - Died: 12 Aug 1911, Escambia County, Alabama the son of William Holly Sr. of this regiment. Wounded at Missionary Ridge, Tennessee on November 25, 1863. Source: Keith Janes
http://www.rootsweb.ancestry.com/~alcwroot/soldier_files/soldiersba.htm