Eunice is a distinctive girls' name in United States, ranking #1509 in 2005 with 138 recorded births. The name reached its all-time peak in 2004 with 212 births ranking #1082. Since 1996, the popularity has decreased by 23.3%. In 2005, approximately 1 in every 13,389 girls born was named Eunice. FALLING Recent data shows the name is currently falling.