Formally, it's known as New York, New York. The main part most people think of as NYC is formally known as Manhattan.
Of course, formerly it was known New Amsterdam. (The tense of your question suggests you meant formerly and not formally. Learn to spell.)
Under the Dutch flag it was called New Amsterdam.
New Amsterdam.
New Amsterdam
New Amsterdam
New York used to be New Amsterdam.
It was once called New Amsterdam.
New York was once called "New Amsterdam" because the Dutch owned New York.
New York City
It is now called New York.
No the city was once New Amsterdam in New Netherlands.
New York City is a part of New York State.
New York City.
New York New York New York
New York City
New York City
New York City is located at the southern edge of New York State. It is sometimes called, "the City of Southern New York."