Israel is the name that was given to YAACOV AVINU (which means Jacob, our father) that is the third out of three fathers of the jewish nation, it was given to him after he survived in a struggle against an angel . because of this he is called israel, because he was among (שרה עם) an angel, but the bible refers to it like he was among the God (אל) .
Among a God = שרה עם אל = ישראל .
That's the origin of the name according to the bible .