In 2 Nephi 20:1 we find the following:
Hearken and hear this, O house of Jacob, who are called by the name of Israel, and are come forth out of the waters of Judah, or out of the waters of baptism, who swear by the name of the Lord, and make mention of the God of Israel, yet they swear not in truth nor in righteousness.
According to Amy Hardison, anciently when one made a covenant, one received a new name. Perhaps the greatest of all covenant blessings is expressed in Isaiah 43:1 in the promise given to covenant Israel: "Thus saith the Lord that created thee, O Jacob, and he that formed thee, O Israel, Fear not: for I have redeemed thee, I have called thee by thy name; thou art mine." Jacob is one of the covenant fathers with whom God established, or reestablished, the Abrahamic covenant, and "Israel" is Jacob's covenant name.
When we enter into Christ's church by covenant, we receive the name of Christ. In ancient times, a name was more than an identifying label. Your name was your essence, what you were all about, your identity rather than just your identification." Thus, to take on Christ's name is both a privilege and an obligation. [Amy Blake Hardison, "Being a Covenant People," in Covenants Prophecies and Hymns of the Old Testament, pp. 31-32]