Twelve Step fellowships have a stated tradition and culture that says; Anonymity is the spiritual foundation of all our traditions, ever reminding us to place principles before personalities.
What this means in practice is simply that only first names are used, no records are kept of attendance or membership, no personal information is shared by others, contact details are never distributed, & etc.
Of course, people being people, this principle is sometimes broken. But, in the main it protects their members from stigma, victimization and recriminations.
On a spiritual level anonymity protects the 12-Step member from becoming a ‘big-shot’ both in the fellowship and in public. Additionally, members generally refuse to publicly become known as a member of a 12-Step group in humility and to avoid adverse publicity if they should go back to their active addiction (drinking, drugging etc).
Sometimes Hollywood takes over and it seems like good publicity to reveal ones membership of, say Alcoholics Anonymous. But this carries no spiritual endorsement of humility. Some have broken their anonymity at the eventual expense of their sobriety.
Thus, the individual alone decides just how much personal anonymity to observe with family, friends and employers, and with other A.A. members as well as.