Our ancestor Pieter(2) Pietersen was first reported in the marriage records of the Old Dutch Church of Kingston in 1679 as Pieter Pietersse and his patronymic Pietersen denotes that he was “the son of Pieter.” It was originally presumed that his father was the cadet listed as Pieter Petersen on the passenger manifest of the Dutch ship De Bonte Koe in 1660. Almost 340 years later it was discovered that his father was indeed named Pieter, but he was Pieter(1) Carstensen of Husum (or Nordstrand) indicating, perhaps, that Pieter(1) Carstensen’s father may have been baptized Carsten or Karsten, but this has not yet been confirmed.
The children of Pieter(2) Pietersen and Rebecca Traphagen (as well as Pieter(2) Pietersen himself) were variously reported with the patronymic spelled Pieters, Pieterse, Pietersen, Pietersz, Pieterz and Pieterszen. It seems that the first time that a member of the family adopted a surname in compliance with the British mandate to abolish the Dutch patronymic system was August 13, 1699 when Pieter(2) Pietersen was reported as Pieter Pieterse Noordstrand. The following year the family began to adopt different versions of a surname. They composed one presumably referring to a locale in Holland – “oost” for east, “rand” for bank, side, or edge: the personal suffix, “er”, and frequently, “van” for from – Oostrander or van Ostrander. Anglicized, this would mean “Eastbanker”, or “Eastsider”. But as with patronymics, the spelling of surnames was far from standardized. Among the variations and at times exotic spellings to be found in church and public records are:
• Ostrandar, Ostranda, Van Noortstrande, Van Noorstrant, Van Nostrandt, Van Nostrant, Van Ostrand, Van Nostrunt, Vanostran, Osterander, Ostervanter, Ostranck. Ostrancer, Ostronder, Ostronden, Ostrandt, Ostrandter, Oustrande, Osatrander, Onstrander, Osstander. 
More than a century went by before the variants disappeared and Ostrander emerged as the favored spelling, but the exact rationale for the adopted surname remains a mystery. Nevertheless it is evident that the surname originated in Ulster County, NY and is unique to the descendants of Pieter(2) Pietersen and Rebecca Trapahgen.