It seems Cook's initial choice had actually been Point Keppel (named after Augustus Keppel, a Lords Commissioner of the Admiralty), but instead he used Keppel later when he named Keppel Bay. The name first appeared on chart 1070, prepared by Captain Phillip Parker King in 1845.
Initially, Cook intended to call the location Point Keppel after Augustus Keppel, a Lords Commissioner of the Admiralty. However, he later chose to use "Keppel" for the bay itself, which was first documented on chart 1070 created by Captain Phillip Parker King in 1845.