Eunice (Εὐνίκη) combines the Greek eu (good) and nikē (victory) — meaning "good victory." In the New Testament, Eunice is the mother of Timothy and the daughter of Lois (2 Timothy 1:5).
Eunice peaked at #133 in the U.S. in 1929. Eunice Kennedy Shriver (1921-2009) founded the Special Olympics.
Eunice 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 Eunice reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.