Monserrat is a distinctive girls' name in United States, ranking #829 in 2003 with 294 recorded births. The name reached its all-time peak in 2014 with 498 births ranking #592. Since 1996, the popularity has increased by 374.2%. In 2003, approximately 1 in every 6,214 girls born was named Monserrat. FALLING Recent data shows the name is currently falling.