Anyone descended from Cors Pietersz, ancestor of most if not all of the Vroom families and some of the Corsons (variously spelled) in the US and Canada, should know that his name wasn't Cornelius. Cors and Cornelius are not interchangeable.
There is no record of his using the name Vroom or any variant of it. Given occasional clerical error, he is by far referred to as Cors Pietersz, Pietersz being the Dutch form of Peterson. The surname "Vroom" appears in later generations, perhaps first among his grandchildren by his son Hendick Corsz.
Of course, if someone knows of a document in which "Vroom" appears earlier, please post.
The only documented reference to Cors' origin in Europe is undoubtedly to the town of Langeraar in the Netherlands ("Corst Pietersz, van Langerheer" as a clerk wrote it). There is no clear reason to think he was not Dutch by birth. There has been much posted on the internet by one individual claiming a French origin, but the reasoning for it is weak and convoluted, in my opinion and that of others familiar with available evidence.
Doug Sinclair