The dream where God talked to Abimelech scared him and he feared for his life, and got up in the morning and told all his servants about it, and they most certainly brought this further to the people. The respect and fear for the God of Abraham must have affected all in the area when Abraham or some of his met them in their moving around with all the animals looking for food and water. God prepared the way for His prophet.
Abraham as nomad moved from place to place and he gave Sarah a standing order to tell people that she was his sister. Sarah was Abraham’s half-sister; they were both children of Terah and siblings of Nahor and Haran, they had different mothers, not named in the Bible.