So there are actually archways showing the names of two of the rivers.
Looks like Styx is the blue river and Cocytus is the grey river. I’m guessing the green river, which Hades nicknames “The River of Lost Souls”, is Lethe. Hades mentions how once Hook touches the river, it will make him lost, reducing him to a mindless, tormented husk. That certainly sounds like the river of forgetfulness to me! I just hope that Hook doesn’t end up touching it, spiraling into an amnesia Hook storyline…
Dear God…that’s where they’re going with this aren’t they? Amnesia Hook who forgets all of his sins and becomes the good hearted saint of the show from now on…
"If you go as far as you can see...you will then see enough to go even further." - Finn Balor