Monserrat is a distinctive girls' name in United States, ranking #592 in 2014 with 498 recorded births. The name reached its all-time peak in 2014 with 498 births ranking #592. Since 1996, the popularity has increased by 703.2%. In 2014, approximately 1 in every 3,586 girls born was named Monserrat. FALLING Recent data shows the name is currently falling.