Once God changed Abram’s name to Abraham and shortly afterwards commanded the rite of circumcision, it was from that juncture that Abraham became a Hebrew.
However, there is a debate as to when the word “Hebrew” itself came into use.
Concerning the meaning of the word Hebrew, the general scholarly consensus is that it means “the one who crossed over“.
However, I tend to side with the opinion that is more prevalent among Bible anthropologists and archaeologists.
They contend that the word Hebrew did not come into use until much later in time and that it comes from the oriental word “ipuru“.
Ipuru was used in Canaan and surrounding areas as a term that simply meant foreigners or wanderers who had no specific nation they could call their own.
This makes much more sense to me given that at this point in time Abraham had been away from his home for such a long time.
God had promised Abraham and his descendants the land of Canaan but they had yet to possess it.
So at this stage, from an earthly perspective, Abraham didn’t have a nation he could point to as his own.
To the inhabitants in the surrounding areas, Abraham and his motley crew would indeed appear to be a bunch of nationless wanderers.
However, this is only from an earthly perspective.
From the heavenly perspective outside of physical limitations and time, it was already a done deal.
Abraham was a Hebrew, he was going to inherit the land, and he was going to be the father of multitudes.