What does Acts 10:48 mean?

A room of Gentiles has heard the bare minimum about Jesus when the Holy Spirit decisively comes upon them (Acts 10:34–44). Peter and six other Jewish Christ-followers (Acts 11:12) witness the Gentiles spontaneously speaking in languages they don't know and "extolling God" (Acts 10:46). Peter challenges the six: if the Holy Spirit has accepted these people, the church must as well, in the form of baptism.

There is undue controversy today over whose name believers should be baptized in. Jesus said the Father, the Son, and the Holy Spirit (Matthew 28:19). This is at least the second time Peter has only mentioned Jesus' name (see Acts 2:38). But the wording isn't meant to be used as a magic formula. "The name of" doesn't mean the syllables and sounds need to be just right or the baptism isn't legitimate. In this case, some of the Gentiles are already God-followers (Acts 10:2). The Holy Spirit has already taken the initiative and baptized them with Himself. Peter now identifies them with the Jesus-worshiping church in Jerusalem started by the disciples of Jesus.

When the Holy Spirit fell on the Gentiles, Peter had barely begun to speak (Acts 11:15). The new converts ask him to stay in Caesarea Maritima, probably to finish his teaching. Undoubtedly, they will eventually meet Philip the Evangelist who is either there or on his way (Acts 8:40) and will make Caesarea his home (Acts 21:8). For now, the foremost of Jesus' disciples stays to teach them what they need to know as new believers and validate that they are, indeed, followers of Jesus—an argument he will then take to the church in Jerusalem (Acts 11:1–18).