Molly is the English diminutive of Mary — from the Hebrew Miriam, possibly meaning "beloved" or "bitter" (the etymology is debated). The pet form Molly has been used since the medieval period.
Molly peaked at #80 in 1991 and remains continuously in the U.S. top 300. The character Molly Weasley in Harry Potter and Molly Bloom from Ulysses are major literary bearers.
Molly 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 Molly reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.