Etymologically it derives from the Thaler, which was both a series of coins and a nominal weight or value within the Holy Roman Empire. Different states at different times used different standards, the Reichsthaler, the Conventionsthaler, the Kronenthaler, the Vereinsthaler, etc. but each Thaler standard was generally defined as some fraction of the the Cologne Mark, from around 1/9th a Mark to 1/14th a Mark (or around 20% less than a Troy ounce of silver). It was something close to the equivalent of a $20 bill.

This of course was nowhere near a unified monetary system. The Empire had a lot of competing standards. But a silver coin that was a bit less than an ounce was a desperately needed standard. Between the 16th and 19th centuries a lot of European countries issued variants on the Thaler including the Dutch Daalder and the various Scandinavian Dolar. And of course a lot of German states issued their own Thaler.p

The Thaler/Daalder/Dolar was adopted into English as the Dollar. Neither England, nor its colonies ever minted their own Dollars. But it became a common nickname for any near 1oz silver coin. Dollar was slang, much like buck, greenback, or Benjamins might be today. Shakespeare for example has at least two plays which reference Dollars Macbeth, and The Tempest. It’s an anachronism in Macbeth as no Thalers had been minted in the 11th century. But by the 17th century the word would have been familiar enough to Shakespeare’s audiences.

So when the colonies broke off they were already accustomed to using the word Dollar. In the colonies it almost always referred to either the Dutch Leeuwendaalder or especially the Spanish Real de a Ocho (aka Piece of Eight). A lot of colonial era contracts were issued using Dollars as a unit of currency. In 1776 the Continental Congress authorized the creation of American coins and bills using Spanish dollars as the unit of currency, as shown on this 2 dollar bill. Over time the “Spanish” part fell off such bills, and dollar became the standard unit of currency in the brand new nation.

So to sum up, the US currency is called dollar because Congress was tying its debts to Spanish currency that was itself mimicking a common coin from Germany.

I drew this primarily from The History of Money by Jack Weatherford. For further reading you may want to look at The Ascent of Money: A Financial History of the World by Niall Ferguson, Money: The Unauthorized Biography by Felix Martin, From Barter to "Bitcoin" - An Overview of Our: Economic History, Monetary System, & Currency Crisis by Mike Thornton