Wouldn't Greater Amsterdam sound better?
Yes, it sure would. However, Greater Amsterdam refers to another, smaller region. Specifically, Greater Amsterdam is a COROP region. In the words of Wikipedia, "A COROP region is a division of the Netherlands for statistical purposes, used by Statistics Netherlands, among others. The Dutch abbreviation stands Coördinatiecommissie Regionaal Onderzoeksprogramma, literally the Coordination Commission Regional Research Programme. These divisions are also used in the EU designation as NUTS 3."