Many sources credit Abraham Ortelius as the first to map and name the islands. In fact, even PBS (Public Broadcasting Service) has this to say:
In 1570, mapmaker Abraham Ortelius plotted the Galapagos Islands, calling them the Isolas de Galapagos …
Well, yes and no. Ortelius did indeed put the islands on the map, but as Isolas de Galapagos? Not quite: his 1570 Americae Sive Novi Orbis, Nova Descriptio shows them, and in fact, shows them twice; once as “Ins. de los galepegos” and again as “Ins de los galopegos” (the latter is probably Isla del Coco). But one year earlier, his colleague Gerard Mercator also showed two island groups on his Nova et aucta orbis terrae descriptio ed usum navigantium emendate accomodata, in this case both labelled “y: de los galopegos.”
But even Mercator was not the first to show and name the islands, for a ca. 1535 untitled vellum chart at the Library of Congress shows “ys. de galapagos.” This may be the first appearance of the islands' name, but it may not be the first appearance of the islands—or at least of one of them.
In about 1522-1525, Lorenz Fries published his Tabula Moderna Alterius Hemisphaerii (“Modern Map of the Other Hemisphere”), described by Dr. Frederik Muller in 2012. The Tabula Moderna … displays a single island with an almost illegible “?i?s” label, which Dr. Muller speculates may be “Dihs” or “dins”(or it may be something else—hover over magnifying-glass icon to view). The author notes that “… an island with the same name at the same place” appeared on a 1517 map, now lost, by Pedro Reinel. It is known today by a 1935 copy, which Dr. Muller does not identify.
But is this island a representation of one of the Galápagos Islands? One argument in favor of this is its placement with respect to the so-called “Unfortunate Islands”—Ins. Infortunate on the Fries map, which today are Islas San Félix and San Ambrosio. Then and now, the former is on or close to the equator, the latter on the Tropic of Capricorn and the two are separated by about ten degrees, as indicated on one of the detail images at the above URL.
To briefly argue against a Galápagos connection, Fries' lone island is about 20 degrees (about 1,400 miles) west of the mainland, while Galápagos is actually only about half that distance away. But a closer look warrants some reconsideration. Note that the Tropic of Cancer touches the continental west coast at about 245° and the equator does the same at 285° (both longitudes are east of Cádiz, Spain). The difference of 40 degrees is in excess of the actual separation of about 16 degrees.
But now, slide the Tropic of Cancer crossing eastward, until its separation from the equatorial crossing is about 16 degrees, thus agreeing with the actual placement of both. In doing so, Fries' island moves eastward until it is slightly more than 10 degrees distant from the mainland, and this in turn closely agrees with the actual location of Galápagos, as also indicated on one of the detail images mentioned above. As a further consideration, there are no other islands on or near the equator until one reaches the western Pacific, much too far to be represented by this one.
So, is “?i?s” actually the first appearance of an island in the Galápagos chain? The evidence, such as it is, suggests that perhaps it is. If the same island and name are indeed on Reinel's 1517 map, then that is the earliest known appearance. Otherwise, it's the Fries ca. 1522-1525 map. But in either case, conclusive proof one way or another must wait until we discover what that four-character label actually means and, where did it come from? It may be a long wait.