This is the third in a series of posts on Vatican II and the Sacraments. What did the Council say regarding the sacrament of Penance (i.e. Reconciliation, Confession)? It certainly did do away with it, although the Council did call for its form to be revised to better express the sacrament's reality. The Council did not recommend renaming the sacrament (which it consistently referred to as Penance) in any way; that is not to say that "Reconciliation" or "Confession" are bad or opposed to Vatican II, but that we should not eschew the name "Penance".
Sacrosanctum Concilium (1963), Constitution on the Sacred Liturgy
72. The rite and formulas for the sacrament of penance are to be revised so that they more clearly express both the nature and effect of the sacrament.
Lumen Gentium (1964), Dogmatic Constitution on the Church
11. Those who approach the sacrament of Penance obtain pardon from the mercy of God for the offence committed against Him and are at the same time reconciled with the Church, which they have wounded by their sins, and which by charity, example, and prayer seeks their conversion.
26. [Bishops] regulate the discipline of Penance...
Orientalium Ecclesiarum (1964), Decree on the Eastern Catholic Churches
27. Without prejudice to the principles noted earlier, Eastern Christians who are in fact separated in good faith from the Catholic Church, if they ask of their own accord and have the right dispositions, may be admitted to the sacraments of Penance, the Eucharist and the Anointing of the Sick.
Christus Dominus (1965), Decree on the Pastoral Office of Bishops
29. Pastors should also be mindful of how much the sacrament of Penance contributes to developing the Christian life and, therefore, should always make themselves available to hear the confessions of the faithful.
Presbyterorum Ordinis (1965), Decree on the Ministry and Life of Priests
5. By Baptism men are truly brought into the People of God; by the sacrament of Penance sinners are reconciled to God and his Church; by the Anointing of the Sick, the ill are given solace; and especially by the celebration of Mass they offer sacramentally the Sacrifice of Christ. ... In the spirit of Christ the Shepherd, they must prompt their people to confess their sins with a contrite heart in the sacrament of Penance, so that, mindful of his words "Repent for the kingdom of God is at hand" (Mt 4:17), they are drawn closer to the Lord more and more each day.
13. This is true in a special way when in the performance of their duty in the sacrament of Penance they show themselves altogether and always ready whenever the sacrament is reasonably sought by the faithful.
18. The ministers of sacramental grace are intimately united to Christ our Savior and Pastor through the fruitful reception of the sacraments, especially sacramental Penance, in which, prepared by the daily examination of conscience, the necessary conversion of heart and love for the Father of Mercy is greatly deepened.