When Jesus told His disciples to baptize in the name of the Father and of the Son and of the Holy Spirit, I think that those who believe that God is a Trinity of Divine Persons see this as one God and not three distinct beings. How do Unitarians interpret this, if the Person referenced as the Son by Jesus is just Himself (i.e. not divine) and not the Second Person of the Trinity, is that Person interchangeable with other prophets? Why baptize in the name of the Father and anyone else?
Note: unitarians can believe that Jesus is divine, as that word is vague and does not need mean someone is God. Angels can be considered divine, the Logos (if understood as not God) can be considered as divine, and even humans can be considered in some sense divine.
Answer: The first step for a unitarian can be to note that Matthew 28:19
"Therefore go and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit" (Berean Study Bible)
simply mentions three things (Father, Son, Holy Spirit) and doesn't claim they are all God, much less articulate finer points of trinitarian theology.
"The mention of the Father, Son and holy spirit together in one context only shows that these three exist. [... while the] doctrine of the Trinity states that the Father, Son and “Holy Spirit” together make “one God” and that the three “Persons” are co-equal and co-eternal, and that doctrine is not stated in this verse."
The second step is to explain why baptizing is done for more than just the name of the Father.
To do this, it helps to explain what the term 'name' means. As the commentary continues (ibid.):
"“name.” A study of the biblical culture and language shows that in this context the word “name” primarily stood for “authority,” and doing something in the “name” of a person or persons who had great authority was very common."
Indeed, Matthew 28:18, which immediately precedes the Great Commission, says
"Then Jesus came to them and said, “All authority in heaven and on earth has been given to Me."
So Jesus' name is included because he has been given all authority by God. As the commentary states (ibid.)
"Given God’s ultimate authority and power, Christ’s exalted position as the risen Messiah and Lord, and the power of God to believers via the holy spirit, which Jesus spoke of at the Last Supper, it makes sense that Jesus would mention all three of them here in Matthew 28. [... Jesus is telling the Apostles] to baptize in the “name” (authority) of the Father, Son, and holy spirit, and they did that."
So the answer is that the Father, Jesus, and the Holy Spirit are all important, and although Jesus is not God, he has been given authority by God - unlike other prophets.