The matter is clear. Since all three are distinct persons, each one of them, except maybe Holy Spirit, got his own name:
- God the Father from the very beginning is called "Yahweh" (Jews and, later, so called christians lost the exact pronunciation of their God's name)
- Son's precious name is "Jesus"
- The Holy Spirit is simply called "The Holy Spirit"
YHWH is the Name of all Three Persons, not the Father only. Many times the New Testament references and alludes to the Old Testament where the Tetragrammaton is used and the text is being applied to Christ. The most notable example I can think of is the Christological hymn in Philippians 2, that every knee will bow and every tongue confess that Jesus Christ is Lord to the glory of God the Father. The hymn alludes back to Isaiah, where YHWH says that every knee will bow and every tongue swear by His Name (Isaiah 45:22-24).
So the Father is YHWH, the Son is YHWH, and the Holy Spirit is YHWH.
But only the Son, becoming flesh by the power of the Holy Spirit in the womb of the Virgin Mary, was given the name Jesus.
Also, not "so-called Christians". The Tetragrammaton wasn't pronounced by ordinary Jews in the first century, and this seems to have been a tradition for several centuries as indicated by the regular use of Adonai and its Greek translation Kyrios both in the Septuagint and in the New Testament. The Samaritans continue a tradition of a pronunciation of the Tetragrammaton, but neither Jews and real actual Christians made normative use of the Tetragrammaton, but were perfectly comfortable using "Lord". This has never been a problem in either Christianity or Judaism.
So the Name Jesus refers to in the Great Commission is simply what He says, "The Father, Son, and Holy Spirit". Jesus isn't referring to names plural, or to some other name than the one He Himself uses; which is why the Church has always invoked the Three-fold Name of Father, Son, and Holy Spirit in the ordinary baptismal rite--as testified as early as the first century Church Manual known as the Didache. Nobody was ever baptized "in the name of YHWH", for example.
-CryptoLutheran