It is possible that Abraham grew up with the knowledge of God the Father, creator. Which is why when he was called by God to get up and leave the land, he knew exactly what he was doing and why, and he knew exactly which God was the true God.
The knowledge handed down, father to son from Adam, Abraham, Isaac, Jacob, Moses. This was their culture that they adhered to (mostly) same as people today.
Of course paganism was rife as was devil worship and all manner of deplorable things.
There were many gods, demons, pagan rituals. These have survived down to our day.
If God only every identified himself as 'I am' in that 'I am God, the Father, the creator, the one true God, even though man has many other gods beside me, ' I AM' God.
And iff Moses grew up with the same knowledge, has handed down through time in their culture, then it is obvious he knew God, as did Abraham.
God's name, personal name, is not relevant or an issue.
It is the jw's that made god's name so important.
They have committed something heinous, they have taken on a name, invented by a monk, involved in spiritism and magic,
and they have attributed this false name to the Most High, One True god, that scripture and history teaches us.
This is my understanding, what I have learned so far on my journey.