Never had the opportunity to see any of these, I'm not that old. Now when it comes to the origins of the names it is quite obvious why a lighthouse is known as a lighthouse, thus it is only the place names and personal names which I shall bother to look at.
Great Pyramid of Giza takes the simplistic but informative place name coming from gaza and meaning 'to cross'. This shows this was a place known as a good crossing point on the Nile.
Hanging Gardens of Babylon is a Greek place name, translated from the Akkadian Babili. It is thought this Babylonian name is a translation of a non-Semitic place name but one unknown and lost in time. However the name Babili is thought to have come about in the belief it meant 'gate of God', this being the meaning of this phrase but not the original name.
Statue of Zeus at Olympia is a gold statue by the sculptor Phidias standing in a place taking its name from Mount Olympos and not to be confused with Mount Olympus, home of the gods, other than the origins of both are completely unknown. Zeus is a very different story and is easily traced. This Greek supreme deity came straight from Proto-Indo-European dewos meaning simply 'god' which is also the source of the Latin deus 'god' and Old Persian daiva 'demon, evil god'. It has also given us wordsin Old Slavonic and Sanskrit meaning 'to gleam, shine' and it is quite likely the idea of an aura around the god gave rise to all these words.
Temple of Artemis at Ephesus, a place in modern Turkey.The name of Ephesus is held to be from Greek ephoros meaning 'overseer' and telling of its importance as a religious site. While Artemis is of unknown origin, the alternative Diana can be traced to the Proto-Indo-European root dyeu meaning, as seen in Zeus, 'to shine'.
Mausoleum at Halicarnassus is thought to represent a place name meaning 'fortress', this supposes it comes from Carian, a language spoken alongside Greek in this area and said to be supported by the inscriptions found here of Alos-o-karnos-o.
Colossus at Rhodes sees the city and the island named from the nymph Rhodos of Greek mythology who bore seven sons sired by Helios, the sun god. Whils she gave her name to the island, three of her grandsons are remembered in three places on the island - namely Camirus, Ialysus, and Lindus.
Pharos Lighthouse at Alexandria is an easy enough place name to explain for it is named after Alexander the Great. Previously this had been known locally as Rhakotis meaning 'that which is built up' and is still a region of the modern city.