Abraham was a Hebrew, descended from Eber. The word "Jew" came into use after the Babylonian captivity, and applied primarily to the tribes of Judah (Yehudi = Jew) and Benjamin.
Well, I believe your opinion is a majority opinion and by its logic, all were Hebrews since creation because Adam ... you know. All came from Adam and none of Abraham's descendants can be independent of his own ancestry.
So, that would mean that every last one of us is a Hebrew as well. Even me. Let us apply the term globally if we are to be correct.
The scripture that I cited (in my opinion only) teaches where God begins the Hebrew people and the "starting point" (or at least the naming point) of their lineage. But, we can't ignore your logic either, so all come from Adam even if God doesn't start with Adam as a naming point.
Genesis 35:10 And 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.
11 And 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;
12 And 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.
Notice the mention of a "
company of nations shall be of thee ..." That's kind of a tip off that there are other nations besides "Jews" included in this nation of Israel.
Now, he does mention Abraham and Isaac, so I get it if that is your basis for understanding Abraham to be a Hebrew also, if that's the "starting point" of the "naming of the lineage" that you think is correct. I don't share that opinion because I start at the "naming point" God first reveals the nation of Hebrews to come of Jacob, now named, Israel
I may be mistaken in that understanding or I may be correct. I don't think that my opinion is held by the majority of believers though. I'll say that much.