Yes. The name is the expression of authority. The disciples were authorized to continue Christ’s work on earth “in His name”—as agents having the power of attorney. Both the power of His presence and the legal authority of His position at the right hand of God are resident in His name. All through the Bible, God has manifested himself by name. The name needed in water baptism is the one showing the completeness of the entire Godhead: the Lord Jesus Christ. 

All through the New Testament baptism was done in the name of the Lord Jesus. 

The use of the name of Jesus was not merely to distinguish Christian baptism from the baptism of John, but to initiate the person into a relationship of submission to Jesus Christ as Lord.  

Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ…. Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost (Acts 2:36, 38).  

 The fullness of the Godhead is expressed in the Lord Jesus Christ. 

Jesus told His disciples to baptize “in the name of the Father, and of the Son, and of the Holy Ghost” (Matthew 28:19).  

 Notice this says “name,” not “names.” What is the name? only in the Lord Jesus Christ is the full power and presence of the Godhead invoked.  

For in him dwelleth all the fullness of the Godhead bodily. And ye are complete in him, which is the head of all principality and power (Colossians 2:9, 10).  

 All things are to be done in the name of Jesus.

Everything His people do is to be done in His name. Healing the sick, casting out demons, preaching—all extension of His work is done in His own name.  

And whatsoever ye do in word or deed, do all in the name of the Lord Jesus, giving thanks to God and the Father by him (Colossians 3:17).  

Just as Israel was baptized unto Moses, we are baptized unto a personal leader. 

We are not baptized into a religion, a moral influence, a metaphysical state, or into some vague essence. Baptism places us into a living relationship with a real person. “The Father, and the Son, and the Holy Spirit” is a term expressing the important truth of the triunity of God, but it is not His personal name. These are but titles. We discover God’s personality in the face of Jesus Christ. 

And, behold, thou shall conceive in thy womb, and bring forth a son, and shalt call his name Jesus (Luke 1:31)