Apparently Samuel Pepys had an Island named after him. But it is not clear if it has been identified. It does appear plausible that this was actually the Falkland Islands as suggested below.
This page contains the complete text of “Cowley's Voyage Round the Globe” which appeared in William Hacke's Collection of Original Voyages published in London in 1699 by James Knapton. Chapters III-VI edited from a typed transcript, courtesy Antony Wenman Cowley. The Galápagos section appears below in bold face type. The four small island insets in left and right margins are on a single sheet in the book—JW.
It was now the Month of December when we set sail from the lat. of 8 deg. North, steering away S. by W. till we came into the lat. of 12 deg. South, then we steer'd away S. W. by W. till we came into Soundings on the Coast of Brazillia, where we had 80 fathom water on a sandy Bank ; then we steer'd away S. W. finding the Sea as red as Blood about the lat. of 40 deg. South, which was occasioned by great Shoals of Shrimps, which lay upon the water in great patches for many Leagues together : We saw also an innumerable company of Seals, which would rise out of the water and blaff like a Dog, with abundance of large Whales, there being more in these Southern Seas, as I may say, by a hundred to one, then we have to the Northward of us. We held our Course S. W. till we came into the lat. of 47 deg. where we saw Land ; the same being an Island not before known, lying to the Westward of us. It was not inhabited, and I gave it the Name of Pepys Island. We found it a very commodious place for Ships to water at and take in Wood, and it has a very good Harbour, where a thousand sail of Ships may safely ride : Here is great plenty of Fowls, and we judge, abundance of Fish, by reason of the Grounds being nothing but Rocks and Sands.
TAMAR,16. (TAMER) (1758 Built by Snook of Saltash. Fire-ship, 1777, when she was renamed PLUTO. Captured 1780) 1764 Cdr. Patrick MOUAT. TAMAR accompanied Capt. Hon. John BYRON in DOLPHIN,24, on a circumnavigation of the globe, sailing from the Downs on 21 June. After leaving Rio de Janeiro on 22 October they sailed south to determine if Pepys Island, reported by William Cowley, the navigator of a buccaneer, in his journal of 1684, existed or not in 47 deg. S. TAMAR and DOLPHIN, sailing parallel courses sufficiently far apart to cover more than 20 leagues, determined that the island was fictional and sailed for Cape Virgins at the northern entrance to Magellan`s Strait, where he watered before proceeding to a group of islands discovered by Capt. DAVID in 1592; the Falkland Strait which separated them had been named by Capt. STRONG in 1689. Capt. BYRON took possession of the islands in the name of George III in January 1765 and called them the Falkland Is. A large bay on the north east corner of East Falkland he named Berkeley Sound and the bay in which he first anchored, Port Egmont. He concluded that, at some 3 deg. further south of Cowley`s latitude, they could be his Pepys Island.
Banks, Joseph, Sir, 1743-1820, 3 January 1769 Series 03: The Endeavour journal of Joseph Banks, 25 August 1768 - 12 July 1771
3. Lat: 47:17, all hands looking out for Pepys's Island; about observing time an appearance was seen to the westward so like an Island that we bear away after it almost assurd that it is Land as the midshipman at the mast head declard; for half an hour, which time he had steadily lookd at it, it did not alter its appearance at all, however about 4 we were convincd that we were in chace of Cape fly away as the seamen call it, no signs of Island or any thing else appearing where it ought to have been.