Multiple Mortal Probations in the Book of Mormon

I am interested in a verse-by-verse analysis of Mosiah 5:7-10 in the light of the Latter-day Saint theological concept known as Multiple Mortal Probations. If you need starter material to begin to understand Multiple Mortal Probations (or MMP as the concept is abbreviated), you can refer to the relevant postings on Issues in Mormon Doctrine. If you don't know the difference between MMP and the idea of reincarnation, please read about it first ;)

Mosiah 5:7-10

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.

And under this head ye are made free, and there is no other head whereby ye can be made free. There is no other name given whereby salvation cometh; therefore, I would that ye should take upon you the name of Christ, all you that have entered into the covenant with God that ye should be obedient unto the end of your lives.

And it shall come to pass that whosoever doeth this shall be found at the right hand of God, for he shall know the name by which he is called; for he shall be called by the name of Christ.

And now it shall come to pass, that whosoever shall not take upon him the name of Christ must be called by some other name; therefore, he findeth himself on the left hand of God.

I will reserve my own interpretation until at least someone else has been given a chance to bite at it.