anonymity
an·o·nym·i·ty
/ˌænəˈnıməti/ noun [ noncount ]
: the quality or state of being unknown to most people : the quality or state of being anonymous
They are trying to protect their child's anonymity.
She enjoyed the anonymity of life in a large city.
She agreed to speak to the reporter only on condition of anonymity. [=only if her name would not be revealed by the reporter]