First: Jacob was renamed Israel before the children of Israel even went to Egypt. God made sure to emphasize the point of the renaming of Jacob to Israel before the children of Israel went to Egypt by emphasizing the name change twice in the book of Genesis.
1. The first time was when Jacob wrestled with God in Genesis 32
Jacob Wrestles with God
22And he rose up that night, and took his two wives, and his two womenservants, and his eleven sons, and passed over the ford Jabbok. 23And he took them, and sent them over the brook, and sent over that he had.
24And Jacob was left alone; and there wrestled a man with him until the breaking of the day. 25And when he saw that he prevailed not against him, he touched the hollow of his thigh; and the hollow of Jacob's thigh was out of joint, as he wrestled with him. 26And he said, Let me go, for the day breaketh. And he said, I will not let thee go, except thou bless me. 27And he said unto him, What is thy name? And he said, Jacob. 28And he said, Thy name shall be called no more Jacob, but Israel: for as a prince hast thou power with God and with men, and hast prevailed. 29And Jacob asked him, and said, Tell me, I pray thee, thy name. And he said, Wherefore is it that thou dost ask after my name? And he blessed him there. 30And Jacob called the name of the place Peniel: for I have seen God face to face, and my life is preserved. 31And as he passed over Penuel the sun rose upon him, and he halted upon his thigh. 32Therefore the children of Israel eat not of the sinew which shrank, which is upon the hollow of the thigh, unto this day: because he touched the hollow of Jacob's thigh in the sinew that shrank. Genesis 32:22-32
2. The second time was when Jacob returned to Bethel after making amends with his brother Esau.
Jacob is Named Israel
9And God appeared unto Jacob again, when he came out of Padanaram, and blessed him.
10And God said unto him, Thy name is Jacob: thy name shall not be called any more Jacob, but Israel shall be thy name: and he called his name Israel.
11And God said unto him, I am God Almighty: be fruitful and multiply; a nation and a company of nations shall be of thee, and kings shall come out of thy loins;
12And the land which I gave Abraham and Isaac, to thee I will give it, and to thy seed after thee will I give the land.
13And God went up from him in the place where he talked with him. 14And Jacob set up a pillar in the place where he talked with him, even a pillar of stone: and he poured a drink offering thereon, and he poured oil thereon. 15And Jacob called the name of the place where God spake with him, Bethel. Genesis 35:9-15
So please miss me with the Egyptology talk. God Himself gave the name of Israel to the descendants of Abraham, Issac, and Jacob. The devil wants to deceive by stealing, killing, and destroying! Thus he copycats God, because He wants to be God, and in turn counterfeits God by introducing corruptions in order to deceive those who love not the truth. Amen.
Second: This is what the Hebrew word for AMEN, which is pronounced (aw-mane') means:
Brown-Driver-Briggs
אָמֵן adverb verily, truly Deuteronomy 27:15,26 (12 t.) 1 Kings 1:36; Nehemiah 5:13; Jeremiah 11:5; Jeremiah 28:6 & doxologies 1 Chronicles 16:36 ( = Psalm 106:48); אָמֵן (ו) אָמֵן Numbers 5:22 (P) Nehemiah 8:6, & in the doxologies Psalm 41:14; Psalm 72:19; Psalm 8:9Psalm 48. ἀμήν = Amen: אֱלֹהֵי אָמֵן Isaiah 65:16 (twice in verse) God of Amen; compare Revelation 3:14, or God of faithfulness, God of truth
I highlighted the key point.
So again, stop leaning on your own understanding and humble yourself before God. Only He can lift the anxiety you have from off your shoulders! For He bears our burdens and takes our heavy yokes! Amen.