The country (and island) is named after the then ruler (Stadhouder), Maurits (Maurice). (and the French named Port Louis after louis XV).
In the Low Countries, stadtholder was an office of steward, designated a medieval official and then a national leader. The stadtholder was the replacement of the duke or earl of a province during the Burgundian and Habsburg period (1384 – 1581/1795).
The title was used for the official tasked with maintaining peace and provincial order in the early Dutch Republic and, at times, became de facto head of state of the Dutch Republic during the 16th to 18th centuries, which was an effectively hereditary role.
For the last half century of its existence, it became an officially hereditary role under Prince William IV of Orange. His son, Prince William V of Orange, was the last stadtholder of the republic, whose own son, King William I of the Netherlands, became the first king of the Netherlands.