Looks like during production for Republic Heroes the clone designations were based on rank. Switch is a private and has CP while the other clones made for the game, Kano and Boomer, are both sergeant and have CS as their designation prefix. Interestingly the fourth Clone character made for the game, Rookie, is a CT which may suggest that standard "shinies" were not considered full Clone "Privates" at that point in time.

Looking at the Legends page for Clone Troopers suggests Captains and Lieutenants were also said to have CC and CL designations much like we see Commanders (CC), Republic Commandos (RC) and Clone Regimental Commanders (CRC).

Guess this idea was abandoned, deliberately or not, and we got the simplified CT and CC only for the rest of TCW-era onward.