New Netherland was the product of the Dutch West India Company that wanted to find a western passage to Asia and later to establish a commercial trading colony on the North America continent. The Dutch West India Company included many people what would today be Belgians. Many of the founders or investors were Flemish Protestants who left Belgium (then belonging to the Catholic Roman Emperor) to go to the Dutch Republic and they helped in establishing the Dutch West India Company which organized the voyages of discovery and colonization to North America. Many people have heard the story about how the GWC agent Peter Minuit purchased Manhattan island from the natives for 60 guilders worth of trade goods. Some think he was Dutch, others think he was German, because he was born in Germany, but Peter Minuit was actually a Belgian and not Flemish but Walloon, his family being from Tournai. They were Protestants though and left Belgium to go to Germany because the Protestants were in power there. It is also not true, I have learned, that he cheated the natives out of Manhattan. He was actually the one cheated because the natives he first bought the island from were not really from there and had no right to sell it and later, when Peter Minuit found this out, he had to buy the island again from the correct owners -so he bought Manhattan twice!
This map has both names "Nova Belgica" and "New Netherland"
In 1664 the New Netherland colony was first taken by the English (the Dutch did not make an effort to protect the colony since it was supposed to be a place of total liberty) but later the powerful Dutch navy defeated the English and restored the colony to Dutch rule in 1673, however, only the next year the Netherlands was attacked by France, England and parts of Germany, exhausted her resources and had to give up the colony to England again who re-named it New York.