Padmavathi is from the Telugu పద్మావతి / Sanskrit पद्मावती (Padmāvatī — padma lotus + vatī possessor — lotus-dweller, she of the lotus). Padmavathi is one of the Telugu + South Indian feminine names — central to traditional Hindu-Indian heritage. Telugu feminine name.
Padmavathi 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.
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In Pythagorean numerology the letters of Padmavathi reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.