Latin Meaning: The name Nala is a Latin baby name. In Latin the meaning of the name Nala is: Olive. SoulUrge Number: 2.Expression Number: 1. People with this name have a deep inner desire for love and companionship, and want to work with others to achieve peace and harmony.atin Meaning: The name Nala is a Latin baby name. In Latin the meaning of the name Nala is: Olive. SoulUrge Number: 2.