According to Nye and Rudd BRM P578 is the original factory designation for the "official" V8 cars, but I suppose it wasn't used in the racing press or programs of the time. I didn't know that P48/57 has been used for all variations in the programmes. I'm not too happy with that name: the Climax-powered cars were simply P57, with a new chassis based on P48 mark II. P48/57 says nothing about the powerplant.

Heaps of names seem to have been used since, like "BRM P57 BRM P56 V8"! In one book William Boddy seems to call the 1962 world champion car "P56" which is really the name of its engine.

To minimise confusion I would prefer factory designations + motor types in Wikipedia (like P57-Climax), and the moderator seems to prefer one page for different variations of the same type. For the individual 1961-62 types the following names would be best:
"P57-Climax"
"P57-V8" (For Lewis+Marsh cars)
"P578 V8"
But I know that most people never use "P578". I would mention them all, and the different name variations, under one page "P57", that would be easiest to information seekers.