Saumya (सौम्या) means "gentle" or "of the moon" (from Soma, the moon god). A traditional Hindu virtue name.
Saumya Tandon (born 1985) is the Indian actress.
Saumya 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 Saumya reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.