Richard Holbrook

From what legit source is he found to be "Lord William" with middle name Richard?

Wikitree: Richard Holbrook (abt. 1480–abt. 1546)
His will was written 19 April 1546 and proved 25 June 1546. It was common practice at that time to bequeath to both the church one attended (in this case Dundry, which was a chapelry) and the mother church (cathedral) (in Wells).
"Richard Holebroke ala Hoges, will, 1546, Dundry, Somerset, England. Abstract is a copy of the document in the Probate Registry found in the New England Historic and Genealogical Society Library, Newbury Street, Boston. Dated 19 April 1546.
I Rychard Holebroke alias Hoges of Dundry. To de Buryed in Dundrey. To my mother churche of saynt Andows yn Welles 4 d. To the chapel of Dundrey 12 d. To every of my god chylidren 2 d. To Thomas Holebrooke my sone 4 oxen. To Joha' Holebrooke dowghter 2 kyen 2 hefferes. To M'gett Hollebroke my dowghter 2 kyen 1 heffer 1 stere and a yerllynge. To elabth Hasyll the wyfe of Thomas Hasyll my doughter 20 s. The resydew to Thomas Holebroke my sone whom I make my executor, and I make John Bong' and Thomas Hasyll my overseers. Witnesses: Thomas Clarke curate of Dundrey, Thomas Froman, William Hardyge. Proved June 25, 1546.
Richard is also found recorded as "Holbrook alias Hoges." His children were:

Richard
Joanna
Margaret
Thomas
Elizabeth (married Thomas Haysell)

• http://www.holbrook-family.com/england.htm
• https://www.genealogy.com/forum/surnames/topics/holbrook/570/
• https://archive.org/details/holbrookalliedfa00lord/page/4/mode/1up?...
• http://www.ourfamilyhistories.org/getperson.php?personID=I16393&tre...