The Name Israel is the God-bestowed (spiritual) name given to Jacob after he prevailed at Bethel, and the name pertains to the continuation of the promises given to Abraham, passed to Isaac and then taken by Jacob when Isaac passed the birthright blessing to him.
Although the names JAcob and Israel may appear to be used more or less interchangeably in places, a careful consideration will reveal the flesh and spiritual natures of the application.
For example, in the treatises given in Gen 48 and 49, we find:
16 The Angel which redeemed me from all evil, bless the lads; and let my name be named on them, and the name of my fathers Abraham and Isaac; and let them grow into a multitude in the midst of the earth.
Here he (Israel) is essentially giving the birthright spiritual blessing to Joseph's sons. (my name be named on them) ie. he is giving away his (God given, spiritual) name of Israel...to Ephraim and Manasseh.
20 And he blessed them that day, saying, In thee shall Israel bless, saying, God make thee as Ephraim and as Manasseh: and he set Ephraim before Manasseh.
21 And Israel said unto Joseph, Behold, I die: but God shall be with you, and bring you again unto the land of your fathers.
22 Moreover I have given to thee one portion above thy brethren, which I took out of the hand of the Amorite with my sword and with my bow.
This 'portion above' represents the first part of the "double portion" given to Joseph.
Then in Gen 49, we find that it is Jacob, (not Israel) that addresses the other of his sons. He (Jacob) then 'blesses' the others not as Israel, because he had already given that name to Ephraim and Manasseh, Josephs two sons.
The other half of the 'double portion' is then given to Joseph in
22 Joseph is a fruitful bough, even a fruitful bough by a well; whose branches run over the wall:
23 The archers have sorely grieved him, and shot at him, and hated him:
24 But his bow abode in strength, and the arms of his hands were made strong by the hands of the mighty God of Jacob; (from thence is the shepherd, the stone of Israel:)
25 Even by the God of thy father, who shall help thee; and by the Almighty, who shall bless thee with blessings of heaven above, blessings of the deep that lieth under, blessings of the breasts, and of the womb:
26 The blessings of thy father have prevailed above the blessings of my progenitors unto the utmost bound of the everlasting hills: they shall be on the head of Joseph, and on the crown of the head of him that was separate from his brethren.