Eszter is the Hungarian form of Esther — from the Hebrew (possibly Persian) meaning "star." The biblical Queen Esther saved the Persian Jews from Haman's plot.
Eszter Tamási (1938-1991) was the Hungarian actress; Eszter Ádám is the singer.
Eszter 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 Eszter reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.