In the Roman Catholic Church, there are many names for this sacrament: the Sacrament of Penance, the Sacrament of Reconciliation, the Sacrament of Confession, etc.
In the Eastern Catholic Church, there are many names for this sacrament as well. The Greeks, Russians, Bulgarians, Ukrainians, and Melkites– to name a few– call the sacrament “The Mystery of Forgiveness.” (You will also note that each of these churches are Byzantine). Other titles for this sacrament include: The Order of Penance, The Ceremony of Forgiveness, The Sacrament of Confession, and Second Baptism.
These names are not regulated and, in many cases, are the result of historical development (for example, you may note that some of the names match those used in the Roman Catholic Church) or theological emphasis (as in the case of the name “Second Baptism”).