For centuries the Octave Day of Christmas (the one-week mark or eighth day), January 1, was marked as the Feast of the Circumcision. The Mass, the Daily Office, the Iconography, all focused on this very Jewish milestone in the life of Jesus.
Then, all of a sudden, people shy away from it, including many of the churches.
Periodically there comes a wave of sentiment against these practices, decrying genital mutilation, the abrogation of the rights of the children, and inflicting needless risk and pain. There is definitely value to this, the practice is not without risk, but that is a discussion best for another forum. Regrettably, lately this has infiltrated the rites of the Church where they shy away from this central act, concentrating on the Name of Jesus, given also at this time. By minimizing and downplaying the circumcision, we miss the important theological lessons, and ironically in an age where the Church is trying not to be anti-Semitic lets in anti-Semitism through revulsion at a rite central to the Covenant.
You heard it here. Denying Jesus' circumcision, downplaying it, is distinctly anti-Semitic and needs to stop RIGHT NOW.
The rite is central to the Covenant between God and Israel. It is as important a marker as Passover and Yom Kippur. For Christians, this unites Jesus and His human nature to the Old Covenant, and therefore in His New Covenant, when we take His nature upon us in Baptism, we are thus grafted into the Covenant with Israel. This is not to say we supercede the Covenant, only that we are grafted in, we are adopted. Likewise, this mitzvot showed the obedience shown not only by St. Joseph, not only by the Blessed Virgin Mary, but also by Jesus Himself to the commandments of God. Jesus is not only God Incarnate, the perfect union of Human and Divine, but He also in His humanity supremely obedient to the Will of the Father in all things, including the commandments of the Law (the interpretation of those Laws is another discussion for another time).
Yes , Jesus received His Name at this ceremony. This name, which literally means, "God is Salvation," receives its power in its meaning, in the hypostatic union of Human and Divine in this Person, and in the absolute and fully-invested obedience of Its holder. And the first step of His personal obedience was the fulfilment of the mitzvot of submitting to the bris milah, the circumcision on the eighth day.
Our Lord told St. Photini at Jacob's Well, "You worship what you do not know; we worship what we know, for salvation is from the Jews." (Jn. 4.22) Let us not gloss over that fact, ever.