Acts 10:46

Then answered Peter, Can any man forbid the water, that these should not be baptized, who have received the Holy Spirit as well as we? And he commanded them to be baptized in the name of Jesus Christ. Then prayed they him to tarry certain days.

Commanded them to be baptized ... Peter did not jump to the conclusion, as many moderns have done, that "Glory be; this does away with baptism altogether"; but, as Bruner noted:

It was impossible for the apostles to associate the gift of the Holy Spirit with anything but baptism; the new converts were immediately baptized.[27]

Moreover, the fact that baptism for Gentiles was necessary to their salvation, no less than it was declared to be on Pentecost, appears in the facts (1) that an angel of God told Cornelius that Peter would tell him words whereby he would be saved (Acts 11:14), and (2) that in all of the words spoken by Peter there was but one commandment, that requiring them to be baptized.

In the name of Jesus ... They are in error who view baptism as here commanded in the name of Jesus to be any different from that enjoined in the great commission, "to baptize ... into the name of the Father, and of the Son, and of the Holy Sprit" (Matthew 28:18-20). Baptism is invariably "in the name of" Jesus Christ, meaning by his authority; but the purpose is the unity of the convert with the sacred triple name of Father, Son and Holy Spirit. The baptism "in the name of Jesus" is at the same time "into the name of the Father, and of the Son, and of the Holy Spirit." As Campbell said, "The authority by which any act is performed must never be confounded with the meaning, or intention, of it."[28]

[27] Frederick Dale Bruner, A Theology of the Holy Spirit (Grand Rapids, Michigan: Wm. B. Eerdmans, Publishers, 1971), p. 193.

[28] Alexander Campbell, Acts of Apostles (Austin, Texas: Firm Foundation Publishing House), p. 76.