Her name is also given as Ann Debard; see for example, the following:
1050Roger Thornton, son of Henry and
Ann Debard, was born Jun 1, 1686. Died before May 6, 1730. Page 531, Richmond Co., VA
Isabella Thornton, Adm. of Roger Thornton's estate, bond made 5-6-1730...Roger married Isabell cir. 1708. Will Bk, page 531.
The foregoing is quoted from a manuscript entitled on "Ancestors and Descendants of Rev. William S. Rogers and Mary Edna Gary Rogers, 1642-1950", by Mary Edna Gary Rogers, who died in 1931 in Elberton, GA at the age of 83 and is assumed to be the compiler of the data in the manuscript.
Another source that gives her name as Ann Debard:
1051Roger Thornton (Jr.) b. June 14, 1725, North Farnham Parish, Richmond, VA, d. in Hancock Co., GA 1797. m. Catherine Lindsey, dau. of Dennis Lindsay, Rev. Sol., Granville, Co., NC. Her mother's name is unknown and was not living in Aug. 1762. (Will of Dennis Lindsey).
Roger Thornton (Jr.) parents: Roger Thornton (Sr.) son of
Anne Debard and Henry Thornton, b. June 1, 1686, m. Isabella cir. 1708. She died after May 6, 1730. He d. before May 6, 1730 (will).
Rogers parents: Henry Thornton b. - d. before 1723, m.
Anne Debard b. - d. living in 1726. Mentioned in Headrights of William Davis on River Potomac, above waters of Puscatawy in 1657.
NOTE by Clayton Heathcock, 22 Nov 2011: Boddie writes that Henry Thornton’s wife was Ann Williams and that she married 2nd Hames Debord after the death of Henry Thornton. Boddie, John Bennett, Historical Southern Families, Vol. XII, "Thornton of Virginia," With Related Families Ransdell, Cox, Atwell, Alford, Williams, Curtis, & Obert, Genealogical Publishing Company, Baltimore, Maryland.