Did David pretend to be insane before Achish or Abimelek?

[tonychanyt]

1 Samuel 21:

10And David rose and fled that day from Saul and went to Achish the king of Gath.

Achish was a Philistine ruler. David was hoping that he could stay under Achish's protection but Achish didn't want him. David thought he was in danger.

13So he changed his behavior before them and pretended to be insane in their hands and made marks on the doors of the gate and let his spittle run down his beard. 14Then Achish said to his servants, “Behold, you see the man is mad. Why then have you brought him to me? 15Do I lack madmen, that you have brought this fellow to behave as a madman in my presence? Shall this fellow come into my house?”

Later, David wrote about this incident in (NIV) Psalm 34:

1 Of David. When he pretended to be insane before Abimelek, who drove him away, and he left.
I will extol the LORD at all times; his praise will always be on my lips.

Didn't David pretend to be insane before Achish and not Abimelek?

Wiki:

this seeming contradiction is easily explainable when you understand that Abimelech would have been his title and Achish, his actual name.

The guy was Abimelech (King) Achish.