Damary is a distinctive girls' name in United States, ranking #15277 in 2011 with 6 recorded births. The name reached its all-time peak in 2007 with 17 births ranking #7471. Since 1996, the popularity has increased by 20.0%. In 2011, approximately 1 in every 293,134 girls born was named Damary. FALLING Recent data shows the name is currently falling.