Before Jacob was born, there were two people whose names were changed:
No longer shall your name be called (יִקָּרֵ֥א) Abram, but your name shall be Abraham, for I have made you the father of a multitude of nations. (Genesis 17:5) [ESV throughout]
And God said to Abraham, “As for Sarai your wife, you shall not call (תִקְרָ֥א) her name Sarai, but Sarah shall be her name. I will bless her, and moreover, I will give you a son by her. I will bless her, and she shall become nations; kings of peoples shall come from her.” (Genesis 17:15-16)
In each case God "called" קָרָא [H7151-qara'] meaning "to call, call out, recite, read, cry out, proclaim" the new name. Also, each new name from God came with promises and described a future characteristic of the person:
Abraham: exceedingly fruitful; a father of many nations; kings shall come from him; establish an everlasting covenant; to be God to him and his offspring; to give all the land of Canaan for an everlasting possession.
Sarah: be blessed; give a son; become nations; kings of all people shall come from her.
God changing a name is done by "calling" by a new name and to giving something new.
Jacob’s Name Change
The first occasion of Jacob's new name comes from a man:
Then he said, “Your name shall no longer be called (יֵאָמֵ֥ר) Jacob, but Israel, for you have striven with God and with men, and have prevailed.” (Genesis 32:28)
The man tells Jacob he will no longer be "called" by this name. The word translated as "called" is אָמַר which means to say speak or utter [H559-'amar]. Thus the English “called” fails to show the man used s different word then God used in naming Abraham and Sarah. In addition, the new name does not come with a promise or some new aspect of character. Rather it reflects something which has already occurred: Jacob has striven with God and men and prevailed.
When God appears to Jacob He says (אָמַר) Jacob will be called (קָרָא) Israel:
And God said (וַיֹּֽאמֶר) to him, “Your name is Jacob; no longer shall your name be called (יִקָּרֵא֩) Jacob, but Israel shall be your name.” So he called (וַיִּקְרָ֥א) his name Israel. And God said to him, “I am God Almighty: be fruitful and multiply. A nation and a company of nations shall come from you, and kings shall come from your own body. The land that I gave to Abraham and Isaac I will give to you, and I will give the land to your offspring after you.”
The language and pattern of naming of Abraham and Sarah are followed. Therefore it is at this point in time Jacob is called Israel. In retrospect, the man "said" what God will do: God will "say" Jacob is "called" Israel.
The relevance of Genesis 35:9
Genesis 35:9 is God's instruction for Jacob to go to Bethel:
God said to Jacob, “Arise, go up to Bethel and dwell there. Make an altar there to the God who appeared to you when you fled from your brother Esau.” (35:10)
God instructs Jacob to return to the place where God first appeared to him. This occurred when Jacob left Canaan to find a wife:
Jacob left Beersheba and went toward Haran. And he came to a certain place and stayed there that night, because the sun had set. Taking one of the stones of the place, he put it under his head and lay down in that place to sleep. And he dreamed, and behold, there was a ladder set up on the earth, and the top of it reached to heaven. And behold, the angels of God were ascending and descending on it! And behold, the Lord stood above it and said, “I am the Lord, the God of Abraham your father and the God of Isaac. The land on which you lie I will give to you and to your offspring. Your offspring shall be like the dust of the earth, and you shall spread abroad to the west and to the east and to the north and to the south, and in you and your offspring shall all the families of the earth be blessed. Behold, I am with you and will keep you wherever you go, and will bring you back to this land. For I will not leave you until I have done what I have promised you.” Then Jacob awoke from his sleep and said, “Surely the Lord is in this place, and I did not know it.” And he was afraid and said, “How awesome is this place! This is none other than the house of God, and this is the gate of heaven.” (Genesis 28:10-17)
After the dream Jacob made a vow:
So early in the morning Jacob took the stone that he had put under his head and set it up for a pillar and poured oil on the top of it. He called the name of that place Bethel, but the name of the city was Luz at the first. Then Jacob made a vow, saying, “If God will be with me and will keep me in this way that I go, and will give me bread to eat and clothing to wear, so that I come again to my father's house in peace, then the Lord shall be my God, and this stone, which I have set up for a pillar, shall be God's house. And of all that you give me I will give a full tenth to you.” (Genesis 28:18-22)
When Jacob returns to the place at which he made his vow, God gives him the name Israel. Also noteworthy is Jacob’s first encounter, which did not come with a name change, included a promise. In comparing this promise with the one at the time he is named Israel, it would appear the only thing added was “kings shall come from his (Israel’s) body.”
Jacob’s name was changed once by God. The man with whom Jacob wrestled was speaking prophetically (or preemptively) about what God was going to say once Jacob returned to Bethel.