The Catholic Church never "changed" its baptismal formula from some other formula to "in the name of the Father, and of the Son, and of the Holy Spirit." This Trinitarian formula, based directly on Jesus's command in Matthew 28:19, has been the standard and normative formula for baptism in the Catholic Church (and most Christian churches) since the early Church.
Here's a more detailed breakdown:
* Matthew 28:19: This is the key scriptural basis: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit..." This verse is understood as a direct command from Jesus to use the Trinitarian formula in baptism.
* Early Church Practice: While there may have been some variations in the very earliest days, the Trinitarian formula was quickly established as the norm. Evidence for this can be found in early Christian writings and liturgical texts.
* Apostles baptising in the name of Jesus: The New Testament also mentions baptisms "in the name of Jesus" (Acts 2:38, 10:48, 19:5). There are different interpretations of this passage. It is possible that the Apostles were simply referring to the Trinitarian formula in a shorter way, or that these baptisms were performed in the name of Jesus as an explicit acknowledgement that the person being baptised was accepting Jesus as their Lord and saviour.
Therefore, the Catholic Church has always taught that baptism should be performed using the Trinitarian formula as commanded by Jesus in Matthew 28:19.