In my limited thinking, the Hebrew culture began to be differentiated beginning with the Exodus, not before.
Willing to be enlightened.
I don't know. Moses seems to have had a pretty good idea they were not Egyptians! I imagine they would be distinguished by names no matter what script was used. One can only wonder in what alphabet were the Ten Commandments written given that the Jews did not adopt the Phoenician alphabet until the 10th century BC. LOL!
Archeological evidence suggets very strongly (multiple sources) that Israelites worshiped a goddess consort of the Hebrew God (El in Israel and Yhwh in Judah) as late as the 8th century BC.
Since there is no similar evidence of any Exodus or wanderings, I would say their differentiation took place gradually living next top the Canaanites.