She seems to have preferred her middle name, Rebecca, and was referred to as Becca and Abecca. See various spellings in her father's will.
In birth records of her children, her name appears as Mary Becca or Mary Becka.
Sources
Christening (June 1744) Groton, Middlesex, Massachusetts Bay Colony, British Colonial America. No source.
profile started by Al Adams, Saturday, March 22, 2014.
North America, Family Histories 1500 -2000
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DNA Connections
It may be possible to confirm family relationships with Mary by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Mary:
Perry-21700 and Perry-4764 appear to represent the same person because: Mary Rebecca Perry was her name at birth, but she was later known mostly as Becca or Abecca. See the birth records of her children at familysearch.org to see her alternate names.