Question: "Why is Jacob called Jacob and Israel alternately in the book of Genesis?"
Answer: Among those individuals renamed in the Old Testament under various circumstances, God Himself renamed only a few. These are Abram (Genesis 17:5), Sarai (Genesis 17:15), and Jacob (Genesis 32:28; 35:9–10), who became known as Abraham, Sarah, and Israel, respectively. The names Jacob and Israel are used alternately throughout Scripture in reference to the second son of Isaac.
Jacob’s birth name, Jacob, means “supplanter, deceiver”; it was given to him because, when Jacob was born as the second of a set of twins, “his hand [was] grasping [his twin’s] heel” (Genesis 25:26). True to his name, Jacob grew up as a conniver, deceiver, and cheat, and he eventually supplanted his brother’s position as heir to the birthright.
After Jacob’s struggle with the Lord at Peniel, the Lord gave Jacob a new name: Israel. And God gave the reason: “Because you have struggled with God and with humans and have overcome” (Genesis 32:28). Later, God appears to Jacob/Israel again in Bethel, reaffirms the name change, and gives him the same covenant that Abraham had received (Genesis 35:9–12). Thus the “heel-catcher” became “one who struggles with God.” It was before he met with God in Bethel that Jacob purposefully put away his idols and purified himself (verse 2).
After the name change, some passages in Genesis refer to Jacob as “Jacob” (Genesis 33:1; 34:7; 35:15; 37:1) and others as “Israel” (Genesis 35:21; 37:3; 43:6; 46:1). Some have suggested that the name Jacob represents his old nature and Israel his new. That is, he is called “Jacob” when functioning in his carnal old nature, but he is called “Israel” when he is acting out of his new nature. There could be limited merit in this suggestion in some passages, and it would parallel the Christian’s experience as presented in Ephesians 4:22–24.
In the end, however, it is best not to make too much of the Jacob/Israel distinction, since some passages include both Jacob and Israel within the same immediate context (e.g., Genesis 37:1–3). Also, there are several psalms that use both names side by side: “Let Jacob rejoice and Israel be glad!” (Psalm 53:6) and “He decreed statutes for Jacob and established the law in Israel” (Psalm 78:5). The parallelism of the poetry identifies the names Jacob and Israel as synonymous, and both names can represent the nation as well as the individual.