Damary is a distinctive girls' name in United States, ranking #10335 in 1998 with 8 recorded births. The name reached its all-time peak in 2007 with 17 births ranking #7471. Since 1996, the popularity has increased by 60.0%. In 1998, approximately 1 in every 220,861 girls born was named Damary. FALLING Recent data shows the name is currently falling.