Depends which one you want to deal with really - both are going to be reluctant to give their real names for different reasons.
Medea will be more paranoid grump and probably need the reminder that she's not in an active war anymore, there's not as much potential damage as she thinks from her identity coming out - so maybe she doesn't need to keep using her Servant Class as a name. She will appreciate treats and wine afterwards.
Mukuro is more likely to have a full on breakdown because since finding out Junko died, she's been doubling down hard on the Junko act - because if she's Junko then Junko isn't daed, and pretending to be her is the last order Junko gave her so she has to stick with it. She'll need some coaxing and reassurance that the world won't end if she lets her actual self out.
no subject
Then she might just be smugDepends which one you want to deal with really - both are going to be reluctant to give their real names for different reasons.
Medea will be more paranoid grump and probably need the reminder that she's not in an active war anymore, there's not as much potential damage as she thinks from her identity coming out - so maybe she doesn't need to keep using her Servant Class as a name. She will appreciate treats and wine afterwards.
Mukuro is more likely to have a full on breakdown because since finding out Junko died, she's been doubling down hard on the Junko act - because if she's Junko then Junko isn't daed, and pretending to be her is the last order Junko gave her so she has to stick with it. She'll need some coaxing and reassurance that the world won't end if she lets her actual self out.