So it seems Pieter did adopt the surname during his lifetime, as evidenced by the 1687 oath of allegiance in King's Co. Back to your original question about the process, I don't know of a formal or uniform process, nor a time schedule. You have the 1687 benchmark, but you can't tell solely from that if that event was the catalyst for adoption or even the first use.
I don't have the William Wyckoff book, but as the name is its main topic, any other documents or clues indicating the surname adoption (such as real estate deeds, wills, court cases) should be covered in the book, unless you have reason to believe he missed something.