Eunique is a distinctive girls' name in United States, ranking #8627 in 2014 with 13 recorded births. The name reached its all-time peak in 2005 with 26 births ranking #4996. Since 1996, the popularity has decreased by 48.0%. In 2014, approximately 1 in every 137,380 girls born was named Eunique. FALLING Recent data shows the name is currently falling.