I was recently asked a question about how surnames were assigned to illegitimate children born in the seventeenth century: Was the surname of the father, or the mother, given to the child? Since illegitimate births were uncommon in New England during the 1600s (about 92% of first children born through 1680 were delivered nine months or more after their parents’ marriage), the illegitimate child could have been given the surname of the mother OR the father, depending on the circumstances. Typically, the illegitimate child would assume the surname of the mother when the identity of the father was unknown. For example, Elizabeth Pederick was the illegitimate daughter of Elizabeth Pederick, baptized in Marblehead 9 December 1694. No father was listed.
While one cannot know based on these records whether Abilene Barnard/Waite was the biological daughter of Richard Waite or his step-daughter, the records do prove that illegitimate children could adopt a surname over time. To prove a more definitive connection between an illegitimate child and a (proposed) father, researchers should expand their research to include records such as probate records, pension files, or church records.