Genesis 17

As the Lord again renews His covenant with Abraham, He says -

"...I am the Almighty God; walk before me, and be thou perfect.
2 And I will make my covenant between me and thee, and will multiply thee exceedingly."  (Old Testament | Genesis 17:1 - 2)

Adding -

"As for me, behold, my covenant is with thee, and thou shalt be a father of many nations."  (Old Testament | Genesis 17:4)

And then the Lord instructs -

"Neither shall thy name any more be called Abram, but thy name shall be Abraham; for a father of many nations have I made thee.
6 And I will make thee exceeding fruitful, and I will make nations of thee, and kings shall come out of thee.
7 And I will establish my covenant between me and thee and thy seed after thee in their generations for an everlasting covenant, to be a God unto thee, and to thy seed after thee."  (Old Testament | Genesis 17:5 - 7)

And then of Abraham's wife -

"God said unto Abraham, As for Sarai thy wife, thou shalt not call her name Sarai, but Sarah shall her name be.
16 And I will bless her, and give thee a son also of her: yea, I will bless her, and she shall be a mother of nations; kings of people shall be of her."  (Old Testament | Genesis 17:15 - 16)

It becomes apparent that many times, as the Lord makes a covenant with man, in a sense it becomes a beginning or rebirth and a new name is given.  We see this with Abraham's grandson as a covenant is made with Jacob, his name is changed to Israel.  We see this also in the Book of Mormon as king Benjamin gives his people a new name as they enter into a covenant with the Lord.

We too take on a new name when we are baptized where we covenant weekly that we -

"...are willing to take upon them the name of thy Son..."  (Doctrine and Covenants | Section 20:77)

And many times a sign, symbol, or token is given to remind us of this new and everlasting covenant.  With this covenant made with Abraham and his seed the Lord instructs -

"This is my covenant, which ye shall keep, between me and you and thy seed after thee; Every man child among you shall be circumcised.
11 And ye shall circumcise the flesh of your foreskin; and it shall be a token of the covenant betwixt me and you.
12 And he that is eight days old shall be circumcised among you, every man child in your generations, he that is born in the house, or bought with money of any stranger, which is not of thy seed."  (Old Testament | Genesis 17:10 - 12)

This token was to be a reminder of this covenant the Lord made with Abraham and his posterity.  Not only just for this covenant, but we learn in the JST that also that -

"....I will establish a covenant of circumcision with thee, and it shall be my covenant between me and thee, and thy seed after thee, in their generations; that thou mayest know for ever that children are not accountable before me until they are eight years old." JST - Genesis 17:11)

It is apparent that there was much mockery and false practices being done in the days of Abraham where we learn in the JST that many people -

"...have turned from the commandment, and taken unto themselves the washing of children, and the blood of sprinkling..."  (JST - Genesis 17:6)