I like it for both genders. It's nice but I prefer
Brooke - which I say you mention. My first thought is
River Song who is a character on the popular
UK show Doctor Who. Apart from that I don't have any associations of the name on people.
It can well work in real life, just like
Brooke,
Sky, and
Meadow, and all of the flower and gem names do.
From your combo stock I like
River Amelia and
River Louisa. Would also like
River Louise,
River Matilda and
River Georgina. Something three syllables that ends in an A would be nice :)