It may seem out of character, but Hugh Hefner of the Playboy empire says he had to reinvent his identity to leave his Puritan roots behind. Hefner told Time magazine that he is a direct descendant of William Bradford, a Puritan who came over on the Mayflower.
Gee, I don't know how to break the news to you Hugh, but there were only two Puritans on the Mayflower, and William Bradford wasn't one of them.
(The two were Christopher Martin and his stepson, Solomon Power, neither of whom left any descendants.) William Bradford and most of the other passengers were Separatists, members of an organization that was quite different from the Puritans.
The Pilgrims, like the Puritans, were from England, but they are not the same religious group. The Pilgrims established the Plymouth Colony in 1620, ten years before the Puritans established the Massachusetts Bay Colony, based in Boston. The two colonies were rivals for many years, partly due to religious differences.
You can read Hugh Hefner's claims to Puritan roots at http://abcnews.go.com/Entertainment/wireStory?id=1180171.
You can read more about the Separatists and their differences with the Puritans at http://www.sail1620.org/discover_myth_pilgrims_not_puritans.shtml.