Yes. Going back, there were 3 generations with the name William, then Edward, then his father was also a William.
William Bourchier
Birthdate: circa 1557
Birthplace: Halstead, Essex, Great Britain
Death: Died July 12, 1623 in Troyes, Aube, Champagne-Ardenne, France
Place of Burial: Tawstock, Devon, England
Immediate Family: Son of John Bourchier, 5th Baron FitzWarin and Frances Bourchier
Husband of Elizabeth Bourchier and Mary Cornwallis, Countess of Bath
Father of Edward Bourchier, 4th Earl of Bath; Richard Bourchier and Frances Bourchier
Occupation: 3rd Earl of Bath, 13th Lord FitzWarin
Edward Bourchier
Birthdate: August 27, 1575
Birthplace: Somerset, England, United Kingdom
Death: Died March 2, 1636 in Tawstock, Devon, England, United Kingdom
Place of Burial: Tawstock, Devon, England, United Kingdom
Immediate Family: Son of William Bourchier, 3rd Earl of Bath and Elizabeth Bourchier
Husband of Dorothy St. John
Father of Bezer; Anne Wrey; Elizabeth Bourchier; John Bourchier, Baron FitzWarin; Dorothy Bourchier and 1 other
Brother of Richard Bourchier and Frances Bourchier
Occupation: 4th Earl of Bath, 14th Lord Fitzwarin
William Brasher/Bradshaw
Birthdate: circa 1595
Death: (Date and location unknown)
Immediate Family: Son of Edward Bourchier, 4th Earl of Bath and Dorothy St. John
Husband of Sarah Bradsher
Father of William Bradshaw/Brazier/Bezer
Brother of Anne Wrey; Elizabeth Bourchier; John Bourchier, Baron FitzWarin; Dorothy Bourchier and Lady Anne Cranfield
William Bradshaw/Brazier/Bezer
Birthdate: circa 1633
Birthplace: Wiltshire, England, United Kingdom
Death: Died 1689 in Worcester, Worcester County, Massachusetts, United States
Immediate Family: Son of Bezer and Sarah Bradsher
Husband of Ann Meredith Brasher / Brashears
Father of William B Bradshaw/Brazier/Breze..., Sr.
William B Bradshaw/Brazier/Breze... (Brashears/), Sr.
Birthdate: March 27, 1675
Birthplace: Baltimore, MD, USA
Death: Died November 6, 1708 in Baltimore, MD, USA
Immediate Family: Son of William Bradshaw/Brazier/Bezer and Ann Meredith Brasher / Brashears
Husband of Elizabeth Clayton Brasher
Father of John Brashier; Thomas Levi Brazier, Sr; William Brazier, JR and Jane Meredith Brazier
Do you have any sources? I ask because the sorry this source shows that Edward Bourchier only had daughters.
http://tinyurl.com/ohzumo3