Who was Alice Stout, daughter of Richard and Penelope, named after?

I found an Internet site that claims Alice was very popular in medieval times (See Chaucer), was scarce for several centuries, then returned to popularity in the Victorian era in time for Alice in Wonderland. Futher checking revealed an Internet site (http://victoria.tc.ca/~tgodwin/duncanweb/documents/names.html) that extracted names for babies born in England in 1620-1629 from a reliable source. (The author was interested in adults in the English Civil War, but names from 1650-1659 England would be skewed by the Puritan success in the Civil War. Thus 1620-1629 is fine for our purposes. A sampling of WorldConnect entries for people born in England in 1620-30 confirmed these were popular names.)
 

The ranking of the popularity of the names of the seven sons of Richard and Penelope are:

#1 John
#4 Richard
#7 James
#21 Peter
#30 Benjamin
#39 Jonathan
#45 David

Likewise for the daughters:

#2 Mary
#5 Alice
#12 Sarah

All ten are common names from the 17^th as well as the 20^th century. All except Richard and Alice are found in the Bible. Interestingly, none are Puritan-like names, such as Eli, Caleb, Hope, and Charity.

The English naming practices for several centuries was to often name the first two babies of each sex after the grandparents and then parents. I just disproved my own theory that Alice was a rare clue to Penelope’s ancestry.

But the question still remains: Who was Alice Stout named after?

And Mary? And Sarah? Why no Elizabeth if Richard’s mother was Elizabeth Bee?