Q1. Is the GMC and the Chevrolet 1/2 ton Hydra-Matic the same Transmission?
A1. Yes, Internal component should be the same.
The GMC & Chevrolet transmission linkage and control linkage are different.

Q2. Is there an official name for this transmission?
Detroit Transmission Hydra-Matic
Fluid coupler, no torque convertor

It has 4 forward speeds and 1 reverse speed.
1-4, All 4 speeds
1-3, 3 speeds used
1-2, 2 speeds used
R, Reverse, Park when engine Off

Hydra-Matic Transmission
1940-1956 ID Plate info
1954 Chevrolet Hydra-Matic ID Plate

1954 GMC Truck Hydra-Matic Transmission Maintenance Manual
1954 Chevrolet Truck Shop Manual
Chevrolet Truck Hydramatic Transmission-Linkage Mechanism
Chevrolet Truck Hydramatic Transmission-Control Mechanism
Chevrolet 1954 Chevrolet Passenger Car & Truck Specifications

Hydra-Matic Transmissions have 3 main housings.
Front Chevrolet Truck Hydramatic Transmission -Flywheel and Fluid Coupling
Center Chevrolet Truck Hydramatic Transmission Assembly-Exploded
Tail Chevrolet Truck Hydramatic Transmission (Reverse Unit)

The front housings were matched to the engine at the factory.
Text casted in the front housing.
Front housing engine ID plate number, should match engine number located on engine boss to the left of the distributor.
Housing Engine ID plate

I have seen Cadillac Hydra-Matic transmission center housings Picture C-54 used on some trucks.