We believe that the command Jesus made in Matthew 28:19 can be best reconciled with Acts 2:38 by realizing that Father, Son and Holy Ghost are titles for the name, that saving name which is Jesus Christ. That is why Peter commanded this in Acts 2:38; "Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost."
Jesus was the Father in creation according to John 1:1 "In the beginning was the Word, and the Word was with God, and the Word was God." Jesus also stated in John 10:30 "I and my Father are one."
Jesus was the Son in redemption. John 3:16 " For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life."
Jesus Christ is the Holy Ghost in regeneration. John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you." Note that the Holy Ghost is being sent "in my name." That name is Jesus Christ.
For further information please listen to link "Baptism in Jesus Name".