Sarojini (सरोजिनी) is from the Sanskrit saroja ("lotus") with the feminine suffix. Sarojini Naidu (1879-1949) was the "Nightingale of India" — Indian independence activist, poet, and orator. Close associate of Gandhi, Nehru, and Jinnah.
Featured on Indian postage and currency.
Sarojini 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 Sarojini reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.