John Calvin Commentary Acts 10:48

"And he commanded them to be baptized in the name of Jesus Christ. Then prayed they him to tarry certain days." — Acts 10:48 (ASV)

And he commanded them to be baptized. It was not necessary that baptism should be administered by Peter’s hand, as Paul likewise testifies that he baptized few at Corinth, for other ministers could take this responsibility upon themselves. When he says, "in the name of the Lord," it must not be restricted to the form, as we have said in the third chapter; but because Christ is the true focus of baptism, therefore we are said to be baptized in His name.

When Luke says, last of all, that Peter was requested by Cornelius and his kinsmen to stay a few days, he commends in them their desire to benefit spiritually. They were, indeed, endowed with the Holy Spirit; but they had not yet reached full spiritual maturity, so that strengthening was still beneficial for them. And, following their example, whenever an opportunity to benefit spiritually presents itself, we must use it diligently; and let us not become swollen with pride, which blocks the path to doctrine.