Monserrat is a distinctive girls' name in United States, ranking #776 in 2007 with 373 recorded births. The name reached its all-time peak in 2014 with 498 births ranking #592. Since 1996, the popularity has increased by 501.6%. In 2007, approximately 1 in every 5,154 girls born was named Monserrat. FALLING Recent data shows the name is currently falling.