Baptism into the Name

In recent times the authenticity of the baptismal formula of Matthew 28:19 has been called into question. It is claimed that the words “in the name of the Father and of the Son and of the Holy Spirit” were never spoken by Jesus to His disciples but rather were added by the Roman Catholic Church at the Council of Nicaea in the year 325. Is this claim true? Did the apostles baptize in this triple name or did they baptize only in the name of Jesus?  Is the baptismal formula a well crafted Trinitarian forgery or is its use of vital importance to the church? Incredible new insights into the reliability and importance of the baptismal formula!