I am not going to quote verse and line.
Whether or not the confession is anonymous or not is up to the person confessing and not the priest. I went to a parish for a long time where the confessional was rigged to make it impossible to be anonymous and a current pastor at my parish mocks in his homilies those who try to give confessions anonymously. I have been at my current parish for 8 years, have not gone to confession there even once because of the priest being vocally against anonymous confession and just this year I have been to confession over 30 times.
I have made sure to tell the people I have sponsored into the RCIA about their rights in this regard and to let them know they can go to confession at another parish if they feel uneasy. One priest got wind of this and told me that if I need to hide behind a screen then I need a shrink, not a priest.