I’ve just had a look at my copy of the book
The Rites of the Catholic Church - as revised by the Second Vatican Ecumenical Council, Volume One published by the Liturgical Press, Collegeville, Minnesota, in 1990. It contains some of the sacramental rites with associated rubrics. For confession, it notes that:
Penitents unknown to the priest are advised to inform him of their state of life, the time of their last confession, their difficulties in leading the Christian life, and anything else that may help the confessor in the exercise of his ministry.
I could be reading it wrong, but to me this suggests that the priest needs to have some knowledge of the penitent in order to do his job properly in confession. If the priest and penitent are genuine strangers to each other then the penitent is to give some back ground knowledge of himself - but this isn’t necessary if the priest already knows the penitent from either inside or outside the confessional. My interpretation of this paragraph is that it isn’t absolutely necessary for the penitent to be absolutely anonymous to the priest.
Just wondering - suppose someone confesed to the same priest regularly. But the priest had to treat each confession as a blank slate, the penitent was completely new to him, a complete stranger and he had no idea who (s)he was. If the penitent was obviously confessing certain sins every time, perhaps because they weren’t making the effort to overcome them, would the priest have to forget about previous confessions every time they confessed, because each one was supposed to be anonymous? Or would he be expected to take previous confessions into account even if this meant he may not be treating the penitent as being completely anonymous? I’m thinking that at some stage the priest may need to say “Look, this sin seems to be a problem and I’m wondering if you’re taking the resolution not to sin again seriously.” Would he be able to do this with strict anonymity?