The "verch William" is her Welsh patronymic -- it means "daughter of William."
Although Welsh women did not use "married" names before the middle of the 16th century, this profile is late enough that her married name is used, that being Pugh.
Which, by the way, is a surname that comes from "ap Huw" meaning 'son of Hugh," a Welsh patronymic.
She is not the daughter of William Pugh. She is the daughter of William ap Owain, or William the son of Owen.