Pomponia is the feminine of Pomponius — a major plebeian Roman gens. Pomponia (1st c. BCE) was Cicero's sister-in-law (wife of his brother Quintus) and a tempestuous letter-writer.
Pomponia Graecina (1st c. CE) was a Roman noblewoman possibly an early Christian convert.
Pomponia 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 Pomponia reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.