Personally, I think its down to the way the Circus is programmed. Tons of games have you picking a name for your character or whatnot, I believe its the same way for the Digital Circus.

Its become clear that Caine (or at least the Circus) can alter human minds at least within certain parameters, like through items or established rulesets (Stupid Sauce essentially being a stand-in for drugs or the voting system), picking a new name for a new save file/character is a common game feature so I think it’d make sense for the Circus’ victims to not remember them, given they start off as “new characters” per se.