Nearly all ordinances, prayers and all we do in the Mormon church are performed in the “name of Jesus Christ” yet the baptismal ordinance is performed in the “name of the Father, the Son and the Holy Ghost”. Can you explain why the difference?
Not only does the baptismal prayer require that the ordinance be performed in the name of all three members of the Godhead, but the ordinance in the temple by which families are sealed together for eternity is also performed in the name of the Father and of the Son and of the Holy Ghost. So we may ask, what is unique about these two ordinances that requires that they be authored by the Father and by the Son and by the Holy Ghost?
The ordinance of baptism contains the covenants enjoined upon the recipient which, if faithfully kept and maintained, guarantees that the person will inherit the celestial kingdom of God–to live for eternity where God dwells–to live in his presence.
Those who are sealed to one another for eternity by the power of the Holy Priesthood, which is the legal authorization to act officially in the very name of the Father and the Son and the Holy Ghost, commit themselves to faithfully abide by the covenants of love, fidelity, true chastity and virtue, and to be equally yoked one to the other as equal partners. If they faithfully fulfill these sacred covenants they will enter into exaltation in the celestial kingdom, receiving a fulness and all the blessings that God has in store for those who truly love Him and keep his commandments. According to the scriptures,
it shall be done unto them in all things whatsoever my servant hath put upon them, in time, and through all eternity; and shall be of full force when they are out of the world; and they shall pass by the angels, and the gods, which are set there, to their exaltation and glory in all things, as hath been sealed upon their heads, which glory shall be a fulness and a continuation of the seeds forever and ever. (D&C 132:19)
We are commanded to pray to the Father in the name of his Son, Jesus Christ. The two prayers that you refer to are not just prayers. They are official acts of the holy priesthood, performed by authorized authorities who represent the Godhead in officiating in their behalf for the salvation and exaltation in the celestial kingdom of his faithful children.