I suspect that, from the point of view of the manufacturer and regulators, you can call the doors anything you like as long as you have a way of identifying each unambiguously.
Interestingly, Airbus itself has changed the way it refers to the doors, at least in its Airport Characteristics manuals, as the narrow-body family has developed.
Initially, for the A319/A320 (left-hand side only, forward to aft), the doors were referred to as:
Fwd passenger/crew door
Emergency exit door [optional on A319]
Emergency exit door
Aft passenger/crew door
Later publications changed that to:
Door 1L
Forward overwing exit
Aft overwing exit
Door 4L
Similarly for the standard A321 (where the emergency exits aren't overwing), initially:
Fwd passenger/crew door
Emergency exit door
Emergency exit door
Aft passenger/crew door
Standard A321 later:
Door 1L
Forward emergency exit
Aft emergency exit
Door 4L
And A321 ACF:
Door 1L
Forward overwing exit
Aft overwing exit
Door 3L
Door 4L
Confused?