Eunice is a distinctive girls' name in United States, ranking #1509 in 2014 with 147 recorded births. The name reached its all-time peak in 2004 with 212 births ranking #1082. Since 1996, the popularity has decreased by 18.3%. In 2014, approximately 1 in every 12,149 girls born was named Eunice. FALLING Recent data shows the name is currently falling.