Yes, I always assumed that it was the influence of ex British Airways Ltd staff which accounted for the wartime fleet carrying either 'British Airways' or just the Speedbird on the nose (but maybe they were trying to save paint/labour/space!)
The sequence with BSAA seems to have been foundation as privately owned British Latin American Airlines, name change to BSAA, Nationalisation and ownership by BOAC, start of service as separate Nationalised Corporation BSAA, period of service with several aircraft losses, reincorporation into BOAC and departure of Don Bennett
Attached a photo of the BOAC desk in the Heathrow Northside Terminal about 1948 showing the graphic attempt to 'unify' the 3 corporations
And for no particular reason some photos of Giles Guthrie (BOAC chairman ca.1964) when he flew BA Ltd first Lockheed 14 service to Warsaw in 1939 (click on pics to enlarge)
Zbiory NAC on-line - prototyp
Zbiory NAC on-line - prototyp
Zbiory NAC on-line - prototyp