Eunice is a distinctive girls' name in United States, ranking #1082 in 2004 with 212 recorded births. The name reached its all-time peak in 2004 with 212 births ranking #1082. Since 1996, the popularity has increased by 17.8%. In 2004, approximately 1 in every 8,661 girls born was named Eunice. FALLING Recent data shows the name is currently falling.