Hannah ma be a second Wife for William or she was Anna Maria known as Hannah;
Christening;
15 June 1806, Melksham, Wiltshire, RACHAEL Gregory, Parents WILLIAM/ANNA MARIA
Siblings;
BRYANT, 06 Nov 1808
JOANNA, 24 March 1811
THOMAS, 10 Nov 1816
GEORGE, 06 Aug 1820 (must have died)
GEORGE, 26 May 1822***
(Source Familysearch.Org)
Trish

EDIT William Gregory age 80, Birth c 1761 is next door to William/Hannah and Family in 1841 Census. Also a Mary Mead age 70 is living with him.
Looks like she was known as Hannah;
Marriage 1805, Melksham, William GREGORY/Anna Maria TRUMAN