The name Gerar in the Bible
When Abraham dwells there, Abimelech is king of Gerar, and when Abraham presents his beautiful wife Sarah as his sister (which was not entirely a lie because they have the same father—Genesis 20:12), king Abimelech has her picked up and delivered to him. Since God has the plan to make Sarah the mother of Abraham's son of promise (Genesis 17:16), Abimelech gets straightened out in a dream and returns Sarah to her husband (20:1-18).
When a famine strikes Canaan, Abraham's son Isaac flees to Abimelech, king of Gerar (Genesis 26:1). When the men of Gerar see Isaac's wife Rebekah they like to know more about her, because she too is very beautiful. Isaac, true to form, explains that she is his sister. And that is a lie because Rebekah is a daughter of Isaac's cousin Bethuel, and a granddaughter of his uncle Nahor.
Isaac and Rebekah get found out when Abimelech looks out his window and sees Isaac and Rebekah having a good time (Genesis 26:8). The verb used to describe how good that time is, is צחק (sahaq), meaning to laugh, play, sport or mock. This verb is also the source of the name Isaac.
Etymology of the name Gerar
The origin of the name Gerar can no longer be established, but there are a few words in the Hebrew Bible that look quite alike. The verb גרר (garar), meaning to drag or drag away, for instance:
To a Hebrew audience, the name Gerar would literally mean Dragging. For a meaning of the name Gerar, Jones' Dictionary of Old Testament Proper Names reads Sojourning, or Lodging Place. NOBSE Study Bible Name List has Region, for no explicable reason.