I strongly doubt that his middle name was Thomas. 'The Early Settlers of Lee County Virginia' says that Thomas was the oldest son and was killed during the Rev War. Based on that book and on the few other records that I have found, none of the family had middle names except possibly their mother who was named Elizabeth (nee smith) but Bedford County records list her as "Jane".

John was the son of Thomas Ely Sr and Elizabeth Smith and here is a list of their children per the book listed above:

Children of THOMAS ELY and JANE SMITH are:

i.THOMAS2 ELY, b. Abt. 1751, Pennsylvania; d. Abt. 1776.
Notes for THOMAS ELY:
Was killed in the Revolutionary War about 1776
ii.WILLIAM ELY, b. March 25, 1753, Pennsylvania;
d. Aft. 1850, Lee Co. VA.
iii.JOHN ELY, b. Abt. 1755, Stafford Co. VA;
d. February 1839, Sugar Run, Lee Co. VA.
iv.ISAAC ELY, b. 1757, Stafford Co. VA;
d. Abt. 1849, Lee Co. VA.
v.RACHEL ELY, b. 1760, Stafford Co. VA;
d. Abt. 1854, Montgomery Co. VA;
m. EDWARD NAPIER, December 28, 1786, Montgomery Co. VA;
b. Abt. 1760, Montgomery Co. VA; d. Unknown.
vi.JANE ELY, b. 1763, Stafford Co. VA;
d. Abt. 1857, Montgomery Co. VA;
m. RENE NAPIER, February 21, 1787, Montgomery Co. VA;
b. 1761, Montgomery Co. VA; d. Abt. 1852, Montgomery Co. VA.
vii.DAVID ELY, b. 1767, Stafford Co. VA;
d. Abt. 1858, Lee Co. VA;
m. SARAH CLAYPOOL, Abt. 1783, Sugar Run,Lee Co. VA;
b. Abt. 1763, Lee Co. VA; d. Abt. 1857, Lee Co. VA.
viii.ROBERT ELY, b. March 09, 1773, Bedford Co. VA;
d. August 27, 1843, Lee Co. VA
ix.JOSEPH ELY, b. November 12, 1775, Bedford Co. VA;
d. November 02, 1827, Lee Co. VA;
m. FRANCIS HIX( HICKS), 1799, Washington Co. VA;
b. November 26, 1778, Washington Co. VA;
d. April 16, 1861, Cane Creek, Lee Co. VA.

FWIW John's wife, Barbara Fry, and Isaac's wife, Catherine Fry, were sisters and the sisters of my wife's 4th GGF George Peter Fry Jr.