Soundharya is from the Sanskrit सौन्दर्य (Saundarya — beauty, grace, harmony). Soundharya is one of the Sanskrit feminine names — central to traditional Hindu Shakta heritage. Sanskrit feminine name reflecting Hindu aesthetic-Tantric heritage.
Soundharya 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 Soundharya reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.