Its use as a girl's name is a recent phenomenon, sparked by the 1984 film Splash, in which Daryl Hannah's mermaid character names herself Madison after seeing a street sign. By the 2000s it was in the U.S. top 5 girl names. It has slipped recently but remains in the top 100.
Madison 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 Madison reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.