Groi, almost unique, decidedly of southern origin, should be a dialectical apheretic form of the surname surname (see SGRO).
The Groi, very very rare, is typically Sicilian, from Cammarata and San Giovanni Gemini in the Agrigento region, should derive from a nickname based on a dialectal alteration of the Greek term archaic sgurós (curly, with curled hair).
Buy a heraldic document with your coat of arms
You may be interested
Verba Volant, Scripta Manent