Achish in Fausset's Bible Dictionary

King of Gath, son of Maoch; called Abimelech, i.e., not merely a king, but also son of a king in the title to Psalm 34: See ABIMELECH for the seeming discrepancy with 1 Samuel 21:10-13; 1 Samuel 27:2. Twice David fled to him. On the first occasion, being recognized as the conqueror of the Philistines, he in fear reigned madness (as the Roman L. Junins Brutus did: Livy, 1:56), and so was let escape to the cave of Adullam. On the second he stayed at Gath, with 600 men, a year and four months, having had Ziklag assigned to him. The unbelieving propensity to calculate probabilities, instead of trusting implicitly to God, misleads even believers into self sought positions of great spiritual danger. "I shall now perish one day by the hand of Saul, there is nothing better for me than that I should speedily escape into the land of the Philistines," said David. This false step on his part necessitated gross lying to the trustful Philistine king (1 Samuel 27:1; 1 Samuel 27:8-12). He finally escaped, only by God's undeserved providential interposition, from having to march with Achish against his own countrymen (1 Samuel 28; 29). Achish, or his son, is again mentioned (1 Kings 2:40)

Link: https://bible-history.com/faussets/A/Achish/