If a child seemed unlikely to live, or if for sound, and sad, anatomical reasons the gender wasn't obvious, it often used to get given the word Creature as its baptismal name - that would be done in a hurry by the midwife.
A child thus named who retained the name would give out a powerful message of neglect, lack of care etc, which might be useful to you.
And at least it was known to happen during the period you seem to be aiming for. Not at all sure that Phaedra would have been used then. Good luck anyway.