Eunique is a distinctive girls' name in United States, ranking #6887 in 2008 with 19 recorded births. The name reached its all-time peak in 2005 with 26 births ranking #4996. Since 1996, the popularity has decreased by 24.0%. In 2008, approximately 1 in every 99,511 girls born was named Eunique. FALLING Recent data shows the name is currently falling.