Jan Janse means Jan, son of Jan. Janse is apatronymand is sometimes written as Jansen. Both suffixes,seandsen, added to a Dutch male name mean son of. There are other suffixes also meaning son of but these two were most often used for Jan in the records I found. Ouderkerk was also spelled Ouderkerck in many historical documents. The English translation of Jan Ouderkerk, as found in his will, is John Ouderkirk, although Ouderkerk remained in general usage for several more generations.
It is reasonable to assume that Jan's father's name was also Jan or Johannes. Because Janse means son of Jan, it stands to reason that Jan's father was named Jan. Also, if Dutch naming conventions were used, the eldest son would be named after the paternal grandfather, In this case, the eldest son was named Johannes, so it would be likely his paternal grandfather's name was Johannes. Both Jan and Johannes are forms of John.
Whether or not Jan Janse's father used the surname Ouderkerk is unknown. Surnamesbegan to be used as early as the 12th century in Europe. It took several centuries before most Europeans had distinguishable surnames that were inherited. Eventually, some patronyms became surnames. For example, Pieterse became Peterson. Other surnames were chosen by the person's occupation (Cooper), location (Woods), nickname or other identifying feature. Ouderkerk can be translated as older church, meaning the family may have originated near an older church. In our case, this could mean that Jan Janse Ouderkerk was John's son John from down by the old church or perhaps the older church if there were more than one church around.
Spelling was inconsistent at this time in history and many names have various spellings throughout the documents found. Part of the reason for this was the transition from Dutch to English within the colonies. Some Dutch sounds have no exact English counterpart. Transcription errors also account for spelling variants. Spelling variants are also the result of poor handwriting of the originators. Jonathan Pearson notes in his Dutch to English translations that he found this to be a particular concern. Lack of consistency of the spelling of names within a single book has been noted, particularly within the body and in the index. Jonathan Pearson's translations of early Albany Dutch records began in 1869, but the publishing of these records didn't occur until some 50 years or so later. It was likely difficult to maintain consistency over such a large body of work without the use of a computer.
Throughout the biography of Jan Janse Ouderkerk, names have been offered in several different variants as that is how they occurred or were translated in the primary source material.