There are multiple origins and meanings for the name:
1. Greek name, derived from the ancient Greek verb (γρηγορέω) [grigoréo] meaning - "alert, watchful, awake, waking, unsleeping" or comes from the late Greek word (γρήγορος) [grigoros] - "quick, fast, rapid, swift, hasty"
2. Derived from the Latin word gregarius meaning - "shepherd, herdsman; grazing herds; simple, ordinary; gregarious"