The presence of the name Jesus Christ is very likely to have been added by Moroni, who would have known the relationship of the person of Jesus Christ to the being who appeared to the brother of Jared. To the brother of Jared we would expect either the Jehovah title, or the Messiah title. There is no way to know which of the two would have been used. The context of the declaration is certainly the atoning mission of the Savior, so it is plausible that the Messiah title was given, although this statement corresponds with the conception from early in the Book of Mormon that Jehovah is God, and that Jehovah is the atoning Messiah.
The declaration that this God is both Father and Son appears to be in this Messianic context. It is in this context that the later King Benjamin declared the Atoning Messiah to be a Father:
Mosiah 5:7
7 And now, because of the covenant which ye have made ye shall be called the children of Christ, his sons, and his daughters; for behold, this day he hath spiritually begotten you; for ye say that your hearts are changed through faith on his name; therefore, ye are born of him and have become his sons and his daughters.