Monica is of disputed etymology — possibly Berber from her North African origin, or from the Latin monere ("to advise, counsel"). Saint Monica (c. 332-387) — Berber Christian mother of Saint Augustine of Hippo whose decades of prayer and weeping are credited with her son's conversion to Christianity at age 32. Their conversation at Ostia just before her death — described in Book IX of Augustine's Confessions — is among the most famous mother-son scenes in Christian literature.
Monica 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 Monica reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.