Sharmila is from the Sanskrit śarmilā (modest, protector, gives joy). Sharmila Roy Pommot — Indian-French historian. Sharmila Bhattacharya — modern Indian-American academic.
Sharmila is a compound name. Its parts are milŭ — each an attested element with a recorded meaning of its own.
Sharmila 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 Sharmila reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.