Monroe is the Scottish surname Mac an Rothaich — "mouth of the river Rotha" (in County Roscommon, Ireland). Monroe Street in Manhattan and across US cities. Monroe County exists in 17 US states. The name Monroe emerged in US top-1000 girls' names in 2012 — directly traceable to Mariah's daughter — and has continued climbing since.
Monroe 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 Monroe reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.