I have located the death record for Jakob Kornellis' daughter Tryntje.  She was 14 years and 6 months at the time of her death.  This is the first recording of the surname KRUIZE.  This is interesting because - up to this time - Jakob had used the patronym Cornellis/Kornellis.  Every other name recorded in the death record is using a patronym. 

So why the sudden change?  Kruize can be a patronym - "son of Kruize".  But we know this not to be factual as Jakob has repeatedly used "Cornellis".  "Kruiz" can also mean "crosses". 

But from this point forward, Jakob and family uses the surname Kruizinga.