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In Matt 28:19, Jesus commanded the apostles to baptize in the name of the Father, and of the Son, and of the Holy Ghost, but we see in Acts of the Apostles that they baptized in the name of Jesus only (Acts 2:38, 8:16, 19:5). Why did the apostles not adhere strictly to the instructions of the Lord concerning water baptism?

Acts 19:1-5 (DRB)

And it came to pass, while Apollo was at Corinth, that Paul having passed through the upper coasts, came to Ephesus, and found certain disciples. 2 And he said to them: Have you received the Holy Ghost since ye believed? But they said to him: We have not so much as heard whether there be a Holy Ghost. 3 And he said: In what then were you baptized? Who said: In John's baptism. 4 Then Paul said: John baptized the people with the baptism of penance, saying: That they should believe in him who was to come after him, that is to say, in Jesus. 5 Having heard these things, they were baptized in the name of the Lord Jesus.

Notice that to be baptized into this "baptism into the name of the Lord Jesus" is baptism into "the Holy Ghost," per St. Paul's question, which implies, or rather necessitates that to be baptized in the aforementioned way is to be baptized into the name of the Holy Ghost also, not literally "I baptize you in the name of the Lord Jesus."

The fact that Peter says what he says in Acts 2:38 even precludes that "in the name of Jesus" is meant as any kind of exclusive formula for baptism. What does it mean then? It simply must be, contextually, a qualified way of identifying the kind of baptism, whether of John or Jesus (except with Jesus' you are baptized "into" Him, not just 'by Him'—and I need not explain the Hebraic use of 'name' here as designating a party or identity to belong to: "believed in His name" =" "believed in him").

So in summary, "in the name of Jesus" isn't the exclusive 'formula' of the baptism mentioned, but rather a primitive identification of that baptism among the different kinds (John's, and perhaps what would have been viewed as a baptism of the Holy Spirit in would be called centuries later the sacrament Confirmation or Chrism: Acts 8:16-17' Mk 1:8).

Sometimes the mutlivalence of meaning in the Greek word εις doesn't help here, since it can be read in the "into" or "in" sense. In English we sometimes associate an "in" + "[name]" formula to be literal, whereas the more Hebraic understanding would be the "into" sense: being radically united with Jesus in baptism:

Romans 6:3 (ESV) Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death?

There is excellent evidence that Matthew 28:19 was added to the text so that the "Trinity" would be in the scriptures (kinda, sorta). The article I cited above begins:

A Baptismal Formula At Variance With NT
The Trinitarian Baptismal Formula appears in only one place in the New Testament: in the canonical Greek Matthew at 28:19. The parallel in Mark 16:15 is otherwise identical except it lacks any trinitarian baptismal formula.

Indeed, every surviving Greek manuscript of Matthew 28:19 has the trinitarian formula. The only non-Greek texts which have a variant that omits it are the Shem-Tob Hebrew Matthew and some old Latin and Syriac texts. Is it possible Matthew 28:19 was fraudulently changed to vindicate trinitarianism because very conveniently every surviving Greek text of Matthew [28:19] dates from 340 AD or later? It clearly could be modified and no one would be the wiser. Only quotes by the church fathers from an earlier time could betray the truth, as indeed seventeen such quotes exist and do so—each one omitting the trinitarian baptismal formula in their direct quotes from Matthew 28:19

The evidence is compelling. And just as compelling is the confusion of the addition itself. It is full of self-contradiction. Name is singular while "Father, Son and Holy Ghost" are three. So what is the singular name of these three? The name of the middle "God" is "Jesus". The modified passage is drivel.