I do believe that this is my family.. I have the name as Jan Claesen Romeyn but as you said it is spelled differently in Holland.
This is the man that was born about 1618 in Holland and was married to Lysbeth Janse..
I believe he came across the ocean on "The Gilded Fox" or "The Fox"but also sailed on the "Guilded Otter"at one point and may have traveled to South America before eventually ending up in New York City which was known as New Amsterdam at the time.
I am descended from their son Stoffel Jan Romeyn who was born about 1641 in Holland as well... I looked at the suggested websites but I don't know the language.. Thank you for the information you have shared..