The ‘Mechs and vehicles of the Royal Brigade commonly wear paint schemes based on the requirement of their current assignment, though for parade and ceremonial purposes the Royal Brigade makes use of a blue, white and red striped scheme, the colors of the Davion family.
Per FM:Federated Suns, page 75
The Brigade’s insignia is a variation on the Federated Suns’ crest, with each RCT adding its own modifications. The Third Guards’ insignia is a phoenix, carrying the Davion sword in its claws. Per FM:Federated Suns, pages 75 and 81.
Between 3059 and 3062, the 3rd switched from their original insignia, shown here: