Eunique is a distinctive girls' name in United States, ranking #7307 in 2010 with 17 recorded births. The name reached its all-time peak in 2005 with 26 births ranking #4996. Since 1996, the popularity has decreased by 32.0%. In 2010, approximately 1 in every 104,549 girls born was named Eunique. FALLING Recent data shows the name is currently falling.