Mary is the English form of the Hebrew Miryam (Miriam) — of uncertain etymology, often glossed as "beloved," "bitter," or "sea of bitterness." The mother of Jesus of Nazareth — the most venerated female figure in Christianity and a major figure in Islam (as Maryam). For most of recorded English history Mary was the single most common feminine name in the language, dominating from the medieval period until the 1960s.
Mary 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 Mary reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.