It is very tempting to construe the use of the singular term ‘name’ in Matthew 28:19 to mean that the three divine beings are also one single deity or one single being; but this is woefully insufficient. The nuances of the English language are as wide and interesting as the limitations of the language. Once upon a time at the university, there were six (6) halls of residence, each with a Hall Christian Fellowship and a president yet collectively they formed the IHCF: Inter-Hall Christian Fellowship (not Inter-Halls; plural) likewise we have PTA: Parent-Teacher Association (not Parents-Teachers; plural). In any case, “…in the name of the Father, and of the Son, and of the Holy Ghost” (KJV) is just a shorter way of saying: ‘…in the name of the Father, and in the name of the Son, and the name of the Holy Ghost.’ The significance of this specific instruction of Jesus can be appreciated from the events recorded in Acts 19:1-6.
The point is, The Word (Jesus) is not the Father, and is also not the Holy Spirit; the Holy Spirit is not the Word, and is also not the Father; the Father is not the Word (Jesus), and is also not the Holy Spirit. When Jesus (the Word) was on earth (right up to the cross), the Father was in heaven, likewise the Holy Spirit; Jesus had to go back to God for the Holy Spirit (the Comforter) to be sent down; (John 16:7). Jesus constantly referred to the Father in heaven; In teaching how to pray, Jesus’s admonishing was: “When you pray, say: Our Father in heaven…” (Matthew 6:9). It is instructive to note that Jesus did not say: “Our Father who is in me.” At another point Jesus cautioned them, saying: “Do not call anyone on earth your father; for One is your Father, He who is in heaven.” (Matthew 23:9). In Acts 7:55-56, it is noted that Stephen, full of the Holy Spirit, looked through open heavens and saw the Jesus (Son of Man) standing at the right hand of God.
It is important to note that, the three divine beings (The Father, the Word, and the Holy Spirit) are distinct/separate, and do not come together to form one divine being/deity, but rather that, they are essentially united in purpose and action; they work together harmoniously (in agreement) and interdependently. They can also act concurrently (at the same time) as seen in the creation of man (Genesis 1:26) and other instances. In terms of leadership structure, we can safely say that the Father works through the Word (the Son), and the Holy Spirit; for instance, it is the Father (Supreme God) who sent the others to come down on earth to dwell among us and in us, and we see the leadership role of the Father consistently at play in the scriptures; according to Apostle Paul, God is the head of Christ (1 Corinthians 11:3; see also 15:27-28). Jesus himself declared that: “My Father is greater than I;” (John 14:28). There is however the argument that Jesus only said so because He was Human at that point, and to demonstrate His humility, and that He is equal in status to God the Father, as implied in the declaration by the Apostle Paul in Philippians 2:5-7. What is interesting here is that, the word translated as ‘equal’ is the Greek word isos (ee’-sos) which also means ‘similar,’ ‘as much,’ or ‘like.’ If you consider the ending of verse 4 and the opening of verse 5: “Christ Jesus: who, being in the form of God…” suggests ‘similar,’ and thus, the use of ‘like‘ would be a perfect rendition of the Greek word isos; in this case. In any case, shouldn’t we rather defer to Jesus who was fully divine and fully man, than deferring to Paul who was only fully man? Even then, the problem is not with what Paul originally said, but rather those who translated that into English. If you like to appreciate the difficulties with the translations better, carefully compare what the NIV says in Luke 10:1 with the same verse in the KJV/NKJV; or see the article: ‘The Second Crucifixion;’ you may click here.