I'm trying to find her source map and I am not finding it. I am also finding other 1607 maps that contradict this. Note that I want this to be true because it pisses off Trump fans, but I'm not sure that this was exactly a common view of North America at the time.
Some 1607 examples:
This one is by Mercator. It does seem to call the region New Spain, but that is not the same thing: https://images.squarespace-cdn.com/content/v1/539dffebe4b080549e5a5df5/1681406870328-59NYYF9DTFGLNTPCG2VX/1607-Antique-World-Map-Mercator-typus-orbis-museum-outlets.jpg?format=2500w
Sorry, this one you have to go to the website and it has annoying zoom features: https://fineartamerica.com/featured/1-vintage-map-of-the-world-1607-cartographyassociates.html
Note, I'm not saying the map is a fake or anything. I have no idea about its authenticity. But it does not seem to be the name the majority of cartographers were using.