Eunice is a distinctive girls' name in United States, ranking #1503 in 2013 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 2013, approximately 1 in every 11,935 girls born was named Eunice. FALLING Recent data shows the name is currently falling.