You might be thinking of the Saint Regis River in Northern New York.
More likely, it might be the Saint Lawrence River, which was called the Kaniatarowanenneh by the Mohawk and Kahnawáˀkye by the Tuscarora Tribe. The river is connected through several lakes, and it's name changes through it's course. From the source, south to it's mouth it is variously called North River, Saint Louis River, Lake Superior, Saint Mary's River, Lake Huron, Saint Clair River, Lake Saint Clair, Detroit River, Lake Erie, Niagara River, Lake Ontario, and the Saint Lawrence River. See the link I have provided for a good picture of how this came to be.
The Saint Lawrence River forms part of the International Border between Ontario, Canada, and the state of New York
The Saint Lawrence river is the longest river in New York. The Saint Lawrence river is 744 miles long.
The major rivers in New York State are the Saint Lawrence River, Mohawk River, Oswegatchie River, Black River, Ausable River, and Chenango River.
New York
What's is the name of New York State and the river after himslef
Saint Lawrence River
The Saint Lawrence River forms the boundary between Ontario, Canada, and New York State.
New York
The Saint Lawrence River flows northeastward from the eastern end of Lake Ontario to the Gulf of Saint Lawrence. The first stretch of the river forms the border between Ontario (Canada) and New York State (USA); the rest of the river lies in Québec.
d) Saint Laurence (38%)
The Hudson River is named after explorer Henry Hudson.
Hudson River
The major river in New York is the Hudson River. It is 314 miles long that flows through the eastern part of New York state. It was named after Henry Hudson. Some other rivers in New York are the Mohawk River and Genesee River.