The Dutch were much slower than the English in adopting surnames as we know them. Patronymics in New Netherland (present day New York) ended theoretically under English rule in 1687 with the advent of surnames, but not everyone followed the new guidelines.
The most common Dutch naming custom was that of patronymics, or identification of an individual based on the father's name. For example Jan Albertszen (who later took the surname Bradt) is given the patronymic of Albertszen, after his father, Albert. Albertszen means son of a man named Albert. So Jan's name can be read as "Jan, the son of Albert"
The patronymic was formed by adding -se, -sen, or -szen. Daughters would very often have the ending -x or -dr. added. For example, Geesjie Barentsdr. (Barentsdochter) is named after her father Barent.
An individual could also be known by his place of origin. Cornelis Antoniszen, who also used the surname Van Slyke, was known in some records as 'van Breuckelen', meaning 'from Breuckelen' (Breuckelen being a town in the Netherlands).
The place-origin name could be a nationality, as in the case of Albert Andriessen from Norway and the ancestor of the Bradt and Vanderzee families. He is recorded in many records as Albert Andriessen de Noorman, meaning Albert, son of Andries, the Norseman.
We also see naming differences over the generations. Albert's sons and daughters took the surname Bradt except for his son Storm, born on the Atlantic Ocean during the family's voyage to the New World. Storm took the surname Van Der Zee (from the sea) and this is the surname his descendants carry.
An individual might be known by a personal characteristic. Vrooman means a pious or wise man; Krom means bent or crippled; De Witt means the white one.
Sometimes an occupation became the surname. Smit=Smith; Schenck= cupbearer, Metsalaer= mason. An individual might be known by many different 'surnames' and entered in official records under these different names, making research difficult unless you're aware of the names in use.
For example, Cornelis Antoniszen Van Slyke mentioned above, is found in records under the following names:
* Cornelis Antoniszen
* Cornelis Teuniszen (Teunis being the diminuitive of Antony)
* Cornelis Antoniszen/Teuniszen van Breuckelen
* Cornelis Antoniszen/Teuniszen Van Slicht (this might have been a hereditary family name based on an old place of origin)
* Broer Cornelis (nickname given him by Mohawks)
Remember that there are tremendous variations in spelling of these names, and changes from Dutch to to English record keeping in the New World affected the spelling even more.
Now that we understand patronymics, how do we record the individual in our genealogy program? A good rule of thumb is to decide what name the individual is found under in official records. Use that name but be sure you record the source for each notation you make and record the name exactly as found in that specific source. It is okay for example to show a man as Cornelis Antonissen in your genealogy program, but show his sons and daughters with their surname of Van Slyke. If the individual never used the surname himself, you should not add it to his name.