Eunice is a distinctive girls' name in United States, ranking #1142 in 2002 with 182 recorded births. This places Eunice in the top 6% of ranked US girls' names for the year. Its actual usage is classified as Rare. The name reached its all-time peak in 2004 with 212 births ranking #1082. In 2002, approximately 1 in every 9,873 girls born was named Eunice. FALLING Recent data shows the name is currently falling.