Rhea

No, it's named after the Greek Titan Rhea.
She is the wife of Kronos and the mother of Hestia, Demeter, Hera, Aides, Poseidon, and Zeus.
She also is the titan of female fertility, motherhood, and generation.
So no, she has nothing to do with a river!

Etymologists have also suggested that it comes from ερα meaning ground—with metathesis (switching) of the first two letters to get ρεα. It has also been suggested that the name is related to the Greek "pomegranate" (ροα) and is Indo-European in origin.

Excuse me, but I have the name Rhea for my middle name. Yet, I pronounce mine much like the name Rae, for it's also short for Rachel. My name was meant to honor my grandmother who holds the name Rachel. Yet, my family has the most unique combinations of names, we spelled my name R-H-E-A, Rhea, or Rae.

Yes, it's probably something that has to do with rivers because in Portugal we have a word "ria" which means river and it's pronounced the same way as Rhea. And since Portuguese language has its roots in Latin and Greek...