"The Hudson Division of the New York Central was named for the Hudson River it parallels."
Yes, but I think the main reason is that it was originally the Hudson River RR. For a while after they joined, the Central was called the New York Central & Hudson River RR.
"The nickname of the NYC was "Water Level Route" to separate itself from rival Pennsylvania Railroad that had to cross mountains to get to the same destinations. The implied meaning was that the NYC was faster and more reliable since it followed the relatively level pathways of rivers and lakes on its way from New York to Chicago."
NYC ads often used the phrase "The Water Level Route - You Can Sleep". They were making the point that on a Pennsylvania RR from New York to Chicago, you would be jostled during the night as the train went up and down grades - whereas the Central's line was smooth and flat.
BTW re railroad names, IIRC Baltimore and Ohio was built to connect Baltimore and it's east coast port to the Ohio river - not to the state of Ohio. Similarly, I believe the Santa Fe referred to in Atchison, Topeka & Santa Fe refers to the Santa Fe Trail which the railroad followed for part of it's line. The ATSF only reached the city of Santa Fe N.M. on a branch line.