Eunice is a distinctive girls' name in United States, ranking #1603 in 2012 with 135 recorded births. The name reached its all-time peak in 2004 with 212 births ranking #1082. Since 1996, the popularity has decreased by 25.0%. In 2012, approximately 1 in every 13,043 girls born was named Eunice. FALLING Recent data shows the name is currently falling.