Instead of citing "in the name of the Father and of the Son and of the Holy Spirit," Eusebius of Caesarea twice mentioned a variant text of Matthew 28:19,
But the rest of the apostles, who had been incessantly plotted against with a view to their destruction, and had been driven out of the land of Judea, went unto all nations to preach the Gospel, relying upon the power of Christ, who had said to them, “Go ye and make disciples of all the nations in my name.”
Eusebius of Caesarea, Ecclesial History, 3:5:3.
What king or prince in any age of the world, what philosopher, legislator or prophet, in civilized or barbarous lands, has attained so great a height of excellence, I say not after death, but while living still, and full of mighty power, as to fill the ears and tongues of all mankind with the praises of his name? Surely none save our only Savior has done this, when, after his victory over death, he spoke the word to his followers, and fulfilled it by the event, saying to them, “Go ye and make disciples of all nations in my name.”
Eusebius of Caesarea, Oration in Praise of Emperor Constantine, 16:8.
The text in itself is not clear enough. There are theological diversities in the early Church as testified with the extant variant texts. There are two possible interpretations regarding this variant: Unitarians use this variant text to justify their belief that the three manifestations is one and the same divine person, Jesus Christ. Trinitarians read this variant text as a reference to the Second Person of the Holy Trinity in Acts 2:38, "In the name of Jesus Christ." As a Catholic I read this passage not in itself but along with its liturgical usage in the early Church which distinguish the three divine persons explicitly.