He shed His blood for our salvation; it is also the Octave of the feast of the Nativity, and, in the Novus Ordo Rite, the feast of the great Mother of God, whose maternity gives all of us life (CE, Introibo, Wiki). The fact is that the celebration of each of these 'events' is present in the liturgical texts of the feast and what one elects to call it depends upon one's extra-liturgical preoccupations more than anything else. Fr Tierney points out:
It is to be noted also that the Blessed Virgin Mary was not forgotten in the festivities of the holy season, and the Mass in her honour was sometimes said on this day. Today, also, while in both Missal and Breviary the feast bears the title "In Circumcisione Domini et Octava Nativitatis", the prayers have special reference to the Blessed Virgin, and in the Office, the responses and antiphons set forth her privileges and extol her wonderful prerogatives. The psalms for Vespers are those appointed for her feasts, and the antiphons and hymn of Lauds keep her constantly in view.
Already in 1960 the title had been changed to 'Octave of the Nativity of Our Lord', and with the advent of the Novus Ordo, mention of Our Lord's Circumcision was thought to be perhaps too mystifyingly physical... or something; it is not a squeamishness I myself can understand, Holy Mother Church just completing the public celebration of the magnum mysterium of a Virgin's pregnancy and childbirth, the 'product' of Her Conception being Lord of Lords and God of Gods.
In illo témpore : Postquam consummáti sunt dies octo, ut circumciderétur Puer : vocátum est nomen ejus Jesus, quod vocátum est ab Angelo, priúsquam in útero conciperétur.
Today, at the beginning of the civil year, it has been long the custom of invoking the blessings of the Holy Ghost on the Nation and the well-being and prosperity of its people by singing the Veni Creator before the principal Mass of the day. Participation in this act is enriched by a plenary indulgence.
Yesterday, the last day of the civil year, was the feast of Pope Saint Silvester (CE, Introibo, Wiki), by whose name the day is widely known in the countries of Middle Europe, Silvesterabend. The principal Mass began with the singing of the Miserere, in contrition and penitence for all the offenses of the past long year, and concluded with the singing of the Te Deum in thanksgiving for all the many blessings we have received from the Lord in these past twelve months. Participation in this act of thanksgiving is also enriched gratia et misericordia Apostolicae Sedis by a plenary indulgence.