"Ap" is Welsh for "son of"; "Verch" means "daughter of". Morgan ap William (about 1474) was son of William ap Ievan, or, son of Ievan. William was an archer who moved his family to England in service of Henry Tudor, the new King Henry VII.

Morgan Williams anglicized his name so that he could marry Katherine Cromwell, who was daughter of William Cromwell alias 'Smith'.

Morgan Williams and Katherine Cromwell were ancestors of Roger Williams of Rhode Island, Roger Williams who settled Virginia, Robert Williams of Roxbury, Massachusetts, William Williams of Acquackanonk New Jersey, and OLIVER CROMWELL.

One of Morgan and Katherine's sons, Richard Williams, took on the name Cromwell at the behest of Henry VIII and in honor of his Uncle Thomas. Oliver Cromwell was descended from Richard. After the Restoration, having the name Cromwell in England was like having the name Hitler in Germany after World War II, and various branches of the family retook the Williams name.

"Williams" most frequently is of Welsh derivation, and the ancient Welsh genealogies go back to the Bible, where the daughter of a king of Israel was spirited away to present-day Wales, at the time of the Babylonian captivity. She supposedly married a Welsh king, and therefrom come many of the royal connections to Adam and Eve.