The doctrine of the Trinity is encapsulated in Matthew 28:19, where Jesus instructs the apostles: “Go therefore and make disciples of all nations, baptizing them in the name (singular- not names) of the Father and of the Son and of the Holy Spirit.”
In this passage the Father, the Son, and the Spirit are said to share one name, and that name is almost certainly
Yahweh, the personal name of God in the Bible. We know this because the name
Yahweh is applied to both the Father and the Son in the New Testament (cf. the Old Testament parallels to citations such as Acts 2:30–36 with Ps. 110:1 and Phil. 2:10–11 with Isa. 45:19–24).
Jesus himself declares that he is Yahweh (“I AM”). In John 8:58, when quizzed about how he has special knowledge of Abraham, Jesus replies, “Truly, truly, I say to you, before Abraham was, I AM.” His audience understood exactly what he was claiming about himself. “So they took up stones to throw at him; but Jesus hid himself and went out of the temple” (John 8:59).
The parallelism of the Father, the Son, and the Spirit is not unique to Matthew’s Gospel; it appears elsewhere in the New Testament (e.g., 2 Cor. 13:14, Heb. 9:14), as well as in the writings of the earliest Christians, who clearly understood these verses in the sense that we do today—that the Father, the Son, and the Spirit are three divine Persons who are one divine Being (God).
This is a mystery. There are some things that are of God that are not fully comprehensible to the human mind.
catholic.com/thisrock/1997/9704frs.asp