Hi Michelle Hartley,
At least I don't think this is a case where collaborators have not tried "to obtain the correct name." Most of the sources you have been kind enough to list report the first wife of Rev. William Worcester (d. 1662) as Sarah _____.
The references to "Sarah Brown" (and "Sarah Blake," which for our purpose seems an alias of Sarah Brown) can be traced directly to the Worcester manuscript by Gustav Anjou. See G2G http://www.wikitree.com/g2g/68133/gustav-anjou
By observation, those references to "Sarah Pickering" that provide for a source have usually cited _New England Marriages prior to 1700_ (which calls her Sarah ____) and what seems a limited production family file. If the latter had provided further documentation, I presume compilers would have so commented. Early New England families tend to receive good coverage from the fine folks at NEHGS. Their on-line collection of journal articles returns but a few modern entries for the name, Sarah Pickering. These refer to a woman, likely born a bit later, who was the wife of Lt. John Buttolph.[1]
In contrast to these Brown/Blake/Pickering claims, are two modern articles, each of which overview the status of particular, relevant English records about the family. Neither of these articles suggest information by which Rev. William's wife would be known as anything other than Sarah ___. These articles are listed below:
(a) Robert L. V. French and Melinde Lutz Sanborn, "The Rev. William^1 Worcester of Salisbury, Massachusetts: Information on His Family from the Olney, Buckinghamshire, Bishops' Transcripts," TAG 71 (1996):50-51 and
(b) Dean Crawford Smith, “Some Olney Cluster Corrections: Newhall, Farrington, Worcester, Fuller,” TAG 73 (1998): 119-122, for Worcester, p. 122.
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[1] See "Nuggets," The Essex Genealogist_ 26 (2006):37; George E. McCracken, "Thomas Buttolph's Earlier Descendants," TAG 58 (1982):137-8.