Find A Grave contributor Ken Smith has made a suggestion to you regarding your Find A Grave memorial for James Badcock.
James was born in Essex, England about 1580, probably near Wivenhoe. Family tradition says that he was a strict Puritan in his faith, and was forced to flee to Leyden, Holland about 1620, with his wife Mary and four children. Mary’s family name might have been Richards. They stayed in Holland for three years, then came to Plymouth in 1623, arriving in June or July of that year, possibly in the ship “Ann”. However, no record has ever been discovered that anyone named Babcock or Badcock ever sailed on the “Ann” or settled in Plymouth.
James & Mary had another child in Dorchester, but Mary died soon after. He married, probably in Dorchester, a second wife whos name is unknown. They had a son, named Joseph, who moved to Saybrook, Connecticut between 1670 and 1680 and became the ancestor of the Babcock family in Connecticut.
Information from “A Catalogue of the Names of the First Puritan Settlers of the Colony of Connecticut”, by R. R. Hinman and American Ancestry
NOTE: Badcock and other forms were the spellings in previous times before James came from England. Those included Badcook, Badcooke, and Badcocke, according to "The Babcock Genealogy" (by Stephen Babcock, 1832-1916. Pub. New York Eaton & Mains.) "For the first 40 years the surname of James and his sons was usually written Badcock. In the Probate records of John Badcock's estate the name is spelled Babcock, and at that time that spelling seems to have been adopted by the family. The Massachusetts branch of the family appear to have adopted the new spelling still later."
Note: Find A Grave Contributor TeaxasLady gave the following suggestions for James Badcock.
"R.R. Hinman wrote a history of various surnames including Babcock but that publication has been proved to be at best a distortion of many facts. James Badcock did not sail on the "Anne" from Leyden in 1623 and the family line, even though they might have come from Essex, England probably did not originate from Wivenhoe. Stephen Babcock's family history is generally regarded by Babcock family genealogists to be very accurate."