Do you use its birth name? If not, how long has it been since it has heard its old name?

Never. slave does not have a name; it is not a “person”; it is slave. It is primarily:
“566” (short for its registred slave number and its real name now). Can also be
“slave”
“whore”
“slut”
“li’l girl”
Depending on what it deserves and what her Owner wants it to be. it has not heard the old name from its Owner for 16 months. Unfortunately it has to be let out and act outside occasionally. Then it may be talked to by outsiders using its old name. It is told this does not give it its name back.