Eunice is a distinctive girls' name in United States, ranking #1014 in 1999 with 202 recorded births. The name reached its all-time peak in 2004 with 212 births ranking #1082. Since 1996, the popularity has increased by 12.2%. In 1999, approximately 1 in every 8,781 girls born was named Eunice. FALLING Recent data shows the name is currently falling.