Her name may have been Abigail; this is an idea deduced from observing the reoccurrence of this name among the descendants.
Some time after entering the above note, I was informed of a reference to William & Abigail Remington in the East Greenwich Town Council records of Jan 1742/3 (source: Cherry Fletcher Bamberg, compiler & editor of "RI Roots" and "Gleanings.") Therefore, I have made a tentative assumption that this may be William, the son of Thomas & Mary, and that his wife is the Abigail referenced in the East Greenwich records.