An interesting combination of names at this moment: "Neeltje Jaspersz Janse Pietersen Janse". It would be nice to have source for her name. I'm pretty sure that she will turn out to only have a first name and one patronym (many Dutch peopel at that time only had a first name and patronym - no surname; also women in the Netherlands never did and still officially don't take on their husband's surname).
I guess that her patronym was "Pietersen", because "Jaspersz" and "Janse" are currently parts of her husbands name. (her husband was most likely only known as "Jasper Baltes" - someone probably assumed that his fathers patronym "Janse" was the surname).