The name Montserrat is a Latin baby name. In Latin the meaning of the name Montserrat is: Jagged mountain.A mountain in Spain: (Montserrat); a monastery.atin Meaning: The name Montserrat is a Latin baby name. In Latin the meaning of the name Montserrat is: Jagged mountain. A mountain in Spain: (Montserrat); a monastery. SoulUrge Number: 3. Expression Number: 8.