I thought I remembered hearing once a name for when Jesus was baptized. Specifically it was referencing the miracle that God the Father, Son, and Holy Spirit were all directly observed at that time (voice of the Father, physical appearance of both the Son and Holy Spirit). My internet search is unusually ineffective (perhaps I misheard and there isn’t a special name for it). I believe it was “the miracle of ______”. I found that it is celebrated during a feast of epiphany, but that doesn’t sound right.
The answer to your question possibly is in fact linked to the Feast of the Epiphany. For on the Feast of the Epiphany we celebrate three mysteries of Our Lord's life. The [Catholic] Church calls Jesus' changing water into wine at the wedding feast at Cana his first miracle.
The Feast of the Epiphany is the continuation of the mystery of Christmas; but it appears on the Calendar of the Church with its own special character. Its very name, which signifies Manifestation, implies that it celebrates the apparition of God to his creatures.
For several centuries, the Nativity of our Lord was kept on this day; and when, in the year 376, the decree of the Holy See obliged all Churches to keep the Nativity on the 25th December, as Rome did - the Sixth of January was not robbed of all its ancient glory. It was still to be called the Epiphany, and the Baptism of our Lord Jesus Christ was also commemorated on this same Feast, which Tradition had marked as the day on which that Baptism took place.
The Greek Church gives this Feast the venerable and mysterious name of Theophania, which is of such frequent recurrence in the early Fathers, as signifying a divine Apparition. We find this name applied to this Feast by Eusebius, St. Gregory Nazianzum, and St. Isidore of Pelusium. In the liturgical books of the Melchite Church the Feast goes under no other name.
The Sixth of January, therefore, restored the celebration of our Lord’s Birth to the Twenty-Fifth of December; but, in return, there were united in the one same Epiphany, three manifestations of Jesus’ Glory: the mystery of the Magi coming from the East, under the guidance of a star, and adoring the Infant of Bethlehem as the Divine King; the mystery of the Baptism of Christ, who, whilst standing in the waters of the Jordan, was proclaimed by the Eternal Father as Son of God; and thirdly, the mystery of the divine power of this same Jesus, when he changed the water into wine at the marriage-feast of Cana. - The Epiphany of Our Lord
What can we notice at the Feast of the Epiphany and its' Manifestations:
- On this day, the Magi appeared to Jesus barring gifts of gold, frankincense and Myrrh.
- On this day Jesus was baptized and the Holy Spirit descended upon Him.
- On this day Christ performed his first miracle by changing water into wine at the wedding feast at Cana.
At Christ's baptism the Holy Spirit descended upon Him; at our Baptism the Trinity took its abode in our soul. At His baptism Christ was proclaimed the "Beloved Son" of the Father; at our Baptism we become the adopted sons of God. At Christ's baptism the heavens were opened; at our Baptism heaven was opened to us. At His baptism Jesus prayed; after our Baptism we must pray to avoid actual sin.
But, did these three Mysteries really take place on this day? Is the Sixth of January the real anniversary of these great events? As the chief object of this work is to assist the devotion of the Faithful, we purposely avoid everything which would savour of critical discussion; and with regard to the present question, we think it enough to state, that Baronius, Suarez, Theophilus Raynaldus, Honorius De Sancta-Maria, Cardinal Gotti, Sandini, Benedict 14th, and an almost endless list of other writers, assert that the Adoration of the Magi happened on this very day. That the Baptism of our Lord, also, happened on the sixth of January, is admitted by the severest historical critics, even by Tillemont himself; and has been denied by only two or three. The precise day of the miracle at the marriage-feast of Cana is far from being as certain as the other two mysteries, though it is impossible to prove that the sixth of January was not the day. For us the children of the Church, it is sufficient that our Holy Mother has assigned the commemoration of these three manifestations for this Feast; we need nothing more to make us rejoice in the triple triumph of the Son of Mary. - The Epiphany of Our Lord
The Wiki article on Theophany clarifies and confirms to what the OP is speaking.
The feast is called Theophany because at the baptism of Christ the Holy Trinity appeared clearly to mankind for the first time—the Father's voice is heard from Heaven, the Son of God is incarnate and standing physically in the Jordan, and the Holy Spirit descends on Him in the form of a dove.
But there are some who perhaps without regard to language or origin call it the Epiphany.
This feast is also sometimes referred to as Epiphany by English-speaking Orthodox Christians, but that name more properly refers to the Western Christian feast falling on that same day and commemorating the visit of the Magi to the child Jesus. The term epiphany does appear in some of the service texts for this feast, however.
This article from New Advent (Catholic Encyclopedia) sheds more light on the melding of the terms and connects it to His baptism or birth. It agrees that the term theophany is basically correct and comes out from the East (Orthodox) per Hippolytus perhaps or Clement of Alexandria, but because the two dates of baptism and birth are assumed so close (Jan 6 and Jan 10), they explain the subsequent confusion.
So Theophany would be the name of the baptism of Christ wherein the Godhead was present.