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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 :)

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