the song is called New Amsterdam because it was the name of New York when it was founded in the 17th century.
the song starts with a list of famous names, each one directly related to New York city:
Jean-Michel Basquiat was a famous graffiti artist in New York;
Francois Truffaut was a famous French film maker and wrote an article which attacked the current state of French films which was published by a New York publisher (Simon & Schuster);
Bob Dylan started is (superb) career by playing in a music venue called "Cafe Wha?" situated between Bleecker Street and West 3rd Street;
the song is called New Amsterdam because it was the name of New York when it was founded in the 17th century.
the song starts with a list of famous names, each one directly related to New York city: