Not only can I tell you positively that "159" was an official name at Alfa, but you also find "159M" and even "160" referred to upgraded 159s at a certain point in the 1951 season. That 160 name never made it to anything public, as far as I know.
Back to the 6C, the point is that all namings were based on the aborted 6C3000 sedan project. So 6C3000CM has the M standing for the capacity increase, where previous names referred to the season, such as 6C3000C50 (meaning competizione 1950). The "genuine" Discos were C52s.
Now indeed, the most usual nickname internally was "Disco 3500". The "Disco" name improperly borrowed from previous year was used only after the Mille Miglia. Earlier documents just say "3500" or "Sport 3500". I have examples of official documents with "3000CM" back in 1953, but in the same folder you can see it designed as "Disco Volante" or "3.5lt." or "tipo 3000 CM" as well.