Ismini is from the Greek Ismēnē (Ἰσμήνη) — sister of Antigone. Ismene (Ismini in modern Greek) is the daughter of Oedipus and Jocasta in Greek mythology — sister of Antigone, Eteocles, and Polynices. Central to Sophocles's Antigone (c. 441 BCE) and Oedipus at Colonus (c. compliance with authority. figure in classical Greek tragic literature.
Ismini 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.
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In Pythagorean numerology the letters of Ismini reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.