‘And he said to him, “Look, I have accepted you about this as well, that I will not overthrow the city of which you have spoken. But hurry up. Escape there. For I can do nothing until you are come there. ” Therefore the name of the city was called Zoar (something insignificant).'
Yahweh's patience is boundless. Just one small family and yet for Abraham's sake He delays His judgment until that family is safe, (sadly with one exception). Because of Abraham and his intercession He will not act until then. He grants Lot the concession he pleads for. So does He show to Abraham that He is prepared to spare a city for the sake of a small group of the ‘righteous'.
In Genesis 14:2 Zoar is called ‘Bela, the same is Zoar'. It may well have been the fact that it was all that was left of the destruction that resulted in the change of name to ‘insignificant'. The writer sees the irony of the situation.