"And Jesus came and spoke to them, saying, “All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all the nations, baptise them into the Name of the Father, and of the Son, and of the Holy Spirit".(Matthew 28:19)
In this one verse, we have the Three Persons of the Holy Trinity. The Speaker here is the Lord Jesus Christ, Who is giving instructions to the Disciples on the baptism of new believers, after they have been saved. He says that this baptism is to be administered in the “Name”, “of the Father, and of the Son, and of the Holy Spirit”.
It should be noted, that Jesus does not say, in “ta onomata”, in the Greek, which is the plural, “Names”. But, clearly uses the singular, “to onoma”, THE NAME. It might be reasonably asked, that, as there are Three Persons mentioned in this verse, why would Jesus use the singular, “Name”, and not the plural, “Names”? This singular “Name” is common with the Three Persons, the Father, the Son and the Holy Spirit. They share this equally.
When Moses witnessed the spectacular event of the “Burning Bush”, which was not consumed, in Exodus chapter 3, the Lord God spoke to him from the bush, are told him that he had been chosen to deliver God’s people, the children of Israel, from Egypt. Moses asks the Lord, that if he were asked for the identity of this God, what Name should he give them. To which the Lord God Almighty answered, "Ehyeh ’ăsher ’ehyeh", which is best rendered in our English as, “I am Who I am”(verse 14), which means, “Eternal, Self-existing, All-powerful, Creator God”. In fact, the Greek version of the Hebrew Old Testament, which was produced some 150 years before the Birth of Jesus Christ, by the best Hebrew scholars of the day, render the Hebrew text as, “"ego eimi ho on", which is, “I am the Eternal One”. Say to those who ask of you, that “I AM” (’ehyeh), has sent me to you. “The Lord (Yahweh), the God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you.’ This is my name forever” (verse 15). The Hebrew Name of God, “Yahweh”, has its root in the verb, “’ehyeh”, speaking of the “eternal, self-existence” of the God of the Holy Bible, Who is Unique, as He has no equal.
The main Name of the Triune God of the Holy Bible, is “Yahweh”, or, as some use the corrupted form, “Jehovah”. It is this NAME, that Jesus Christ refers to in Matthew 28:19, which is used equally for the Three Persons.
It should also be noted, that, even though Jesus says "Name", (singular), the Greek text that follows is also very important: "tou Patros kai tou Huiou kai tou Hagiou Pneumatos", where the Greek "article" (tou), is repeated, to show that a "distinction" of Persons is meant. (Dr Samuel Green; Handbook to the Grammar of the Greek Testament, pages, 198-199)