Couldn't find actual names of parents but found this source that might be a clue: Genealogical & Family History of Northern, NY
Pages 455-463 : The Salmons were an ancient and chivalrous Scotch family who, during the turbulent period which culminated in the seating of Robert Bruce upon the throne of Scotland (1306), fought valiantly for the preservation of their national independence, and at least one of them, if not more, was knighted by that monarch. In the fourteenth century, the Salmons migrated to England, and settled in Scotland. In 1640 three families of this name emigrated to America, one settling in Massachusetts, another in New Jersey, and the third established themselves in Southold, Long Island. Among the latter was William Salmon, who married the widow of Matthew Sunderland prior to 1649, and had William, John, and other children. The family about to be mentioned are descended from John Salmon, who was presumably of the Long Island family.