Padmini (पद्मिनी) is the Sanskrit word for "lotus pond" or "woman who is like a lotus." Rani Padmini (or Padmavati) was the legendary 13th-century Rajput queen of Chittor, subject of Jayasi's 1540 epic Padmavat.
Padmini is widely used in India.
Padmini 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 Padmini reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.