Rivers is from the Old French rivère (river, flowing water) — historically a surname now used as a modern unisex given name. Sam Rivers (1923-2011) — male; American jazz musician.
Rivers does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Rivers reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.