While Henry Hudson is credited with being the first European to explore the river in 1609, the river already had a name given to it by the Native Americans who lived in the area.
The name "Hudson" was given to the river by Dutch explorers who followed Hudson's path. They called it the "de Rivier van de Heiligen" (the River of the Saints) and "de Noordt Rivier" (the North River), but the name "Hudson" eventually became the official name in English.
So, while Henry Hudson is a significant figure in the river's history, he did not name it.