Port Moresby was named in honour of which admiral?

Port Moresby was named in honour of Admiral Fairfax Moresby.

Moresby was the surname of the British naval family associated with the harbour's European naming history. In 1873, Captain John Moresby surveyed the south coast of New Guinea aboard HMS Basilisk and named the harbour Port Moresby in honour of his father, Admiral Sir Fairfax Moresby.

The younger Moresby was the explorer who carried out the survey; Fairfax Moresby was the admiral being honoured. That distinction explains why John Moresby is a tempting but incorrect answer to this question. Arthur Gordon was a prominent British colonial administrator, while James Cook was an eighteenth-century navigator, but neither gave Port Moresby its name.

The settlement later became the capital of Papua New Guinea. Its name therefore preserves a link to nineteenth-century British naval exploration in the Pacific, even though the city itself has a much older history involving the Motu and Koitabu peoples.