The word 'dollar' referring to a currency is Czech in origin. It comes from the word 'Thaler' or 'Taler'. This itself comes from a valley ('Thal' in Czech or 'Tal' in German) called Joachimsthal, in Bohemia (now Czech). This area was made rich by silver mining in the early 16th century, and the silver coins made there became known as Thalers. There were other versions later in different countries, such as the Scandinavian daler.
In English the word changed into 'dollar' (it can be found in Shakespeare) and was applied not only to the Bohemian Thalers but for other coins, including those from Spain, that looked similar. When Europeans spread across the Americas they often used these Spanish coins, even in North America as there were not enough of the British pounds that the North American settlers originally used. The word 'dollar' was thus a natural choice for the independent American currency.
You can learn more about the history of the dollar here.