“Father,” or “Son,” or “the Holy Spirit” are not names. They are titles. The name of the Father and of the Son and of the Holy Spirit is “Jesus” (Jn 5:43; 17:11; 14:26), and there is only one name (singular).
The name “Jesus” carries authority and honor (Phil 2:9-11). In the name of the Lord Jesus, baptism has the power to heal and make new. God has also manifested His power when believers cast out demons in the name of the Lord Jesus. But it is not merely the recitation of the name that makes baptism effective or drives away evil spirits. It is the presence of the Holy Spirit and the promise of God that manifests God’s power in Jesus’ name.
The name of Jesus Christ is the only one under heaven given to men by which we must be saved (Acts 4:10,12). The disciples always baptized or instructed the people to be baptized in the name of the Lord Jesus (Acts 2:38; 8:16; 10:48; 19:5). In Acts 19:4-5, the believers were re-baptized “in the name of the Lord Jesus.” Only through the name of Jesus is a person’s sin cleansed during baptism (Acts 2:38; 10:43).