New Amsterdam (and the entire colony of New Netherland) was captured by the English, and became part of a large swath of territory King Charles II granted to his brother the Duke of York (the later King James II of England and King James VII of Scotland). That's when the city and colony began to be called New York.
Eboracum is the Latin name for York, England, so on the seal New York is referred to as Novum Eboracum.
York is where Constantine was proclaimed emperor in 306, to tie things back to Istanbul...
Nicely done...