Based on those facts and that authority, the Father only works through Jesus authority now (John 14:26; John 15:16; John 16:23; John 16:26).

Nevertheless, though the Father only works through Jesus’ authority today, who is directing Christ today (Psalms 110:1; 1 Cor. 15:24-28)?  We are commanded to pray to the Father (John 16:23, 26) and the Son will do the work (John 14:13).  Nevertheless, though the scripture says that Jesus will answer the prayer, it also says that the Father will respond to the same prayer (John 15:16).

When all of Jesus’ enemies are subdued under his feet (1 Cor. 15:24-27), then Jesus will also be subject to the Father (1 Cor. 15:28).  The Father put all things under Jesus, and Jesus will give that same authority back to the Father (1 Cor. 15:27-28).

Therefore, though there are two names involved, there is but one authority.  That authority was with the Father until the resurrection, has been with the son since the resurrection, and will return to the Father after the Judgment.  Therefore, in Matthew 28:19 there are not three authorities.  In the sense of authority, there is but one name in that verse.  However, because there are three Beings involved in that one authority, we are to baptize in the name (the one authority) of the Father, Son, and Holy Spirit.