Damary is a distinctive girls' name in United States, ranking #7410 in 2001 with 14 recorded births. The name reached its all-time peak in 2007 with 17 births ranking #7471. Since 1996, the popularity has increased by 180.0%. In 2001, approximately 1 in every 128,611 girls born was named Damary. FALLING Recent data shows the name is currently falling.