Treize,
The Helldiver wasn't given its designation because it was specifically the "Second Curtiss Helldiver." Its designation was purely because it was the second Curtiss SCOUT-BOMBER. The original Helldiver was designated SBC.
The Navy gets even more confusing when different manufacturers built the same aircraft. Corsairs were also built by Goodyear and Brewster, but they received entirely NEW designations (FG-1 for Goodyear's first fighter, and F3A-1 for Brewster's third). The aircraft were identical to their Vought equivalents (IE, the F4U-1A, FG-1A and F3A-1A were all the same aircraft) but the Navy still identified them under these designations.
Oh, and then there's cross-branch usage, where the B-24D became the PB4Y with the Navy, and SBDs in the USAAF were called the A-25.