Eunique is a distinctive girls' name in United States, ranking #5647 in 2001 with 20 recorded births. The name reached its all-time peak in 2005 with 26 births ranking #4996. Since 1996, the popularity has decreased by 20.0%. In 2001, approximately 1 in every 90,028 girls born was named Eunique. FALLING Recent data shows the name is currently falling.