Parentage uncertain. His father's first name may have been Thomas. There is no consensus as to who his mother was. The exact number of children he had, and their names, is also uncertain, except that the William White who was the father of Resolved and Peregrine White was not one of them.

A more or less official consensus can be found here: http://www.massmayflower.org/publications/md/md43/MD43-183-186.pdf

A descendant(?) and namesake, Alexander White, brother of Eleanor White Ruble and brother-in-law of Owen Ruble (also spelled Rubel), was a member of the First Continental Congress in America.