Having taught Dutch in several countries, I've often been asked why Dutch is called, er, Dutch - by Anglophones. After all, the reasoning goes, we call the language of France, French, England, English and Italy, Italian. So why is the language spoken in Netherlands, or Holland as it is sometimes called, not Netherlandish, or Hollandish, but .. Dutch. According to the OED, it goes back to the Middle Dutch term, dutsch, rendered in the authoritative Woordenboek der Nederlandsche Taal as duutsc. This was used to refer to the spectrum of language varieties spoken in the Low Countries and Germany. It is a cognate of Deutsch, the German word for 'German' still in use today, which originally meant 'the language of the people' in contrast to Latin.
In Tudor England, the Anglicized form 'Dutch' was still used to denote language varieties from Germany and the Low Countries. When the Scottish emissary Sir James Melville visited Queen Elizabeth he observed that her 'Dutch' was 'not gud', but we do not know if he was referring to the language of Germany or the Low Countries. Some English-speakers made a contrast between High Dutch, i.e. German and Low Dutch, i.e. Dutch. We find this distinction in the diary of Robert Hooke, who learnt Low Dutch to read the works and letters of Dutch scientists, but also acquired books in High Dutch. The shift towards applying 'Dutch' to languages varieties of the Low Countries gained an impetus with the political independence of the United Provinces.
Today, like English, Dutch has several varieties. The two principal varieties in the Low Countries are Netherlands Dutch (Nederlands-Nederlands) and Belgian Dutch (Belgisch-Nederlands), although these include many sub-varieties. Other varieties include Suriname Dutch and Caribbean Dutch . Indeed, along with Peter Burke, it might be better to talk of 'Dutches' rather than Dutch.
Roland Willemyns, Dutch: Biography of a Language. Oxford: OUP, 2013.
Peter Burke, Towards a Social History of Early Modern Dutch. Amsterdam: AUP, 2005.
Christopher Joby, The Dutch Language in Britain (1550-1702). Leiden: Brill, 2015.