text: "A key point - lost in some of the reporting - is that Catholic priests anywhere in the world already have the power to forgive the sin of abortion. The penitent walks out of the confessional forgiven and reunited to God’s grace.
  The issue here is not the sin itself, but the excommunication, and who can lift it. In the Code of Canon Law that power is reserved to a bishop - unless, as in the United States, he has chosen to extend this authority to his priests.
  In parts of the world where that power had not been granted, the priest would have forgiven the repentant sinner immediately and then have asked the penitent to return at a later time; during that interval the confessor would have secured his bishop’s permission to lift the canonical penalty. (Anonymity, of course, would have been honored, with the identity of the penitent never disclosed.)"  https://cruxnow.com/church/2015/10/12/why-werent-all-priests-able-to-absolve-from-the-sin-of-abortion-already/
  
  So - anonymity preserved.