In #1360, Marten says Dora has gone into a fugue state.
Fugue states, says Wikipedia, include loss of memory and even changes to identity.
They're a possibility in the QC universe. In #1029, Dave admits to the possibility that he's a serial killer and simply doesn't know it. Fugue states are part of QC "reality" and are therefore a legitimate possible explanation for QC phenomena.
Someone with another identity, and amnesia about it, would be caught short by questions about her activities.
In #813, Penelope hems and haws about her off-work life. Every sentence begins with "um" or "uh", unusual for a normally articulate person. She even says "I guess" at one point.
We've never seen Penelope out shopping, or eating, or doing any of the leisure activities Faye and Marten do all the time.
Penelope is uncertain what to say about her time off work because she doesn't know what she does when she's not at Coffee of Doom or at the gym. We've never seen her and Pizza Girl together because she is Pizza Girl: she denies it because she truly does not know that she's Pizza Girl.