Even though Jacob's name change to Israel appears to be quite similar to Abram's name change to Abraham (compare Gen 17:5 with Gen 35:10) in essence, they are very different.  In contrast with Abraham, where the single letter "heh" is added to the existing name, Israel constitutes an entirely new name.  Furthermore, 'Israel' serves as an alternative name for Jacob, in contrast with Abraham which became a replacement!

The Bible describes two instances when Jacob received his new name 'Israel', on his return to his home land, Canaan.

1) After his struggle with the angel, prior to his confrontation with Esau.  (Gen 32:24-30) 
2) Later, during YHVH's revelation to him at Beth-El.  (Gen 35:9-13)

In the second event, we see the connection between the name 'Israel' and the 'election' process, which is the primary theme of Genesis.

The Return to Beth-El

Jacob's return to Beth-El - the site where he received his very first vision some twenty years earlier - marked the prophetic 'highlight' of his return to Canaan.  It was at Beth-El where YHVH first informed him that he was indeed the 'chosen' son, (Gen 28:12-14) and it was there that YHVH had promised to look after his needs during his journey to Laban.

Beth-El was also the focal point of Abraham's journey to Canaan, where he built an altar and 'called out in YHVH's Name.'

Upon Jacob's return, YHVH appeared unto him once again, confirming his election and changing his name to Israel.

"And YHVH appeared again to Jacob on his arrival from Padan Aram, and blessed him: You, whose name is Jacob, shall be called Jacob no more, but Israel shall be your name.  Thus He named him Israel and YHVH said to him: I am El Shaddai, be fruitful and increase ... The land that I have given to Abraham and Isaac I give to you and to your offspring to come..."  (Gen 35:9-16)  

Considering that this was the last time in the book of Genesis where YHVH confirmed the election, (the blessing of "seed and land" - (Gen 12:1-7, 13:14-16, 15:18, 17:7-8, 26:1-5, 28:13)  we can be sure that there was a thematic connection between this name change to Israel and the conclusion of the "election" process!

To understand why specifically this name - Israel - was chosen, we must turn to the first event when Jacob received this name, after his victory over the 'angel'.  

What's in a Name?

Let's take a look at the progression of the events that led up to this struggle.

1. Isaac planned to bless Esau with prosperity and power.
2. Jacob 'stole' Esau's blessing.
3. Jacob 'ran away' to Padan Aram.
4. Jacob 'ran away' from Padan Aram.
5. Jacob prepared for his confrontation with Esau.                         
6. YHVH sent an angel to confront Jacob.
7. Jacob met Esau, bowing to him seven times.

Up until this point, Jacob's life was characterized by his need to employ trickery to acquire what was rightly his.  During his life, he had become an expert at survival, but he lacked experience in 'confrontation,' the trait that Esau was best at.

It may have been for this very reason that Isaac had originally intended to bless Esau, for he understood that in order to establish a nation, leadership was essential.  During his youth, Jacob lacked this characteristic.  Once it had been determined that Jacob was to be the only chosen son, it became necessary for him to develop leadership traits as well.

As Jacob returned to Canaan, he had to confront Esau.  However, from his strategy (Gen 32:13-21) it became quite clear that he was still not ready for it.  In fact, he tried to show Esau that he never actually received the blessing of prosperity and power which he tried to steal.  By bowing down to Esau, Jacob wished to show his brother that the 'stolen blessing' of power and dominion over his brother didn't work.  Again, Jacob was using deception, to cover up the first one.

It was at that point that Jacob's struggle with the angel took place - after his preparation to bow down to Esau, but before the actual confrontation.  This order of events points to a connection between this struggle and that confrontation.

Jacob never had to openly confront Esau but he proved that he was capable of fighting with any 'Esau' if he had to.  

YHVH  tested Jacob's ability to engage in battle with his enemy before he actually met Esau.  This struggle with the 'angel' was extremely difficult for Jacob, and continued all night until the 'break of dawn.'  Although wounded and limping, Jacob emerged victorious from this confrontation, thus earning his new name:

"Your name shall no longer be Jacob but Israel, for you have fought with Elohim (spiritually) and Men (physically) and triumphed."   (Gen 32:28)  

Thus, the name 'Israel' meant triumphant in battle.  Jacob's new name was significant for it reflected his ability to engage head on in battle.  In order to become a nation, this trait - represented by the name 'Israel' - was crucial.

Why Twice?

Earning his new name from the angel was not in itself sufficient for Jacob.  It had to be confirmed to him personally by YHVH, along with his election, at Beth-El (the very site where he was first promised the 'election').  The blessings which Jacob received by deception had to be given to him again properly by YHVH. 

YHVH's blessing to Jacob at Beth-El (Gen 28:1-4) was an exact confirmation of Isaac's blessing to him after the incident of the stolen blessings.  The name 'Israel' marked the conclusion of the election process, and a character trait to later become YHVH's special nation.

The Future

Although Jacob's personality remained dormant for several generations, it remained a part of his character which was passed on to his children Judah and Josepf, along with the leadership. (Gen 49:8-26)

Throughout the rest of the Bible, the name Jacob interchanges with Israel.  This suggests that each name reflects a different aspect of his character.  There were times to act as 'Jacob', and there were times when the more active and nationalistic characteristics of Israel must be employed.  Ultimately, as the prophet Obadiah said, the day will come when:

"Deliverers shall march up on Mount Zion to bring judgement on the Mount of Esau; and the kingdom shall belong to YHVH."  (Obadiah 1:21) 

Because of the significance of the special name  Israel  the election process had to continue for another generation past Isaac, and establish the elimination (rejection) of Esau. 

The Bible clearly tells us that Jacob and Esau cannot co-exist!  

"But upon Mount Zion shall be deliverance, and there shall be holiness; and the house of Jacob shall possess their possessions... and there shall not be any remaining of the house of Esau; for YHVH had spoken it."   Obadiah 1:17-18