How do geological time periods get their names?

Because the British were the most active in the early years, British names are predominant in the geological lexicon. Devonian is of course from the English county of Devon. Cambrian comes from the Roman name for Wales, while Ordovician and Silurian recall ancient Welsh tribes, the Ordovices and Silures. But with the rise of geological prospecting elsewhere, names began to creep in from all over. Jurassic refers to the Jura Mountains on the border of France and Switzerland. Permian recalls the former Russian province of Perm in the Ural Mountains. For Cretaceous (from the Latin for chalk) we are indebted to a Belgian geologist with the perky name of J. J. d'Omalius d'Halloy.

Originally, geological history was divided into four spans of time: primary, secondary, tertiary, and quaternary. The system was too neat to last, and soon geologists were contributing additional divisions while eliminating others. Primary and secondary fell out of use altogether, while quaternary was discarded by some but kept by others. Today only tertiary remains as a common designation everywhere, even though it no longer represents a third period of anything.

Lyell, in his Principles, introduced additional units known as epochs or series to cover the period since the age of the dinosaurs, among them Pleistocene (most recent), Pliocene (more recent), Miocene (moderately recent), and the rather endearingly vague Oligocene (but a little recent). Lyell originally intended to employ -synchronous for his endings, giving us such crunchy designations as Meiosynchronous and Pleiosynchronous. The Reverend William Whewell, an influential man, objected on etymological grounds and suggested instead an -eous pattern, producing Meioneous, Pleioneous, and so on. The -cene terminations were thus something of a compromise.

Nowadays, and speaking very generally, geological time is divided first into four great chunks known as eras: Precambrian, Paleozoic (from the Greek meaning old life), Mesozoic (middle life), and Cenozoic (recent life). These four eras are further divided into anywhere from a dozen to twenty subgroups, usually called periods though sometimes known as systems. Most of these are also reasonably well known: Cretaceous, Jurassic, Triassic, Silurian, and so on.

Then come Lyell's epochs the Pleistocene, Miocene, and so on which apply only to the most recent (but paleontologically busy) sixty-five million years, and finally we have a mass of finer subdivisions known as stages or ages. Most of these are named, nearly always awkwardly, after places: Illinoian, Desmoinesian, Croixian, Kimmeridgian, and so on in like vein. Altogether, according to John McPhee, these number in the tens of dozens. Fortunately, unless you take up geology as a career, you are unlikely ever to hear any of them again.

Further confusing the matter is that the stages or ages in North America have different names from the stages in Europe and often only roughly intersect in time. Thus the North American Cincinnatian stage mostly corresponds with the Ashgillian stage in Europe, plus a tiny bit of the slightly earlier Caradocian stage.

Also, all this changes from textbook to textbook and from person to person, so that some authorities describe seven recent epochs, while others are content with four. In some books, too, you will find the tertiary and quaternary taken out and replaced by periods of different lengths called the Palaeogene and Neogene. Others divide the Precambrian into two eras, the very ancient Archean and the more recent Proterozoic. Sometimes too you will see the term Phanerozoic used to describe the span encompassing the Cenozoic, Mesozoic, and Paleozoic eras.

Moreover, all this applies only to units of time. Rocks are divided into quite separate units known as systems, series, and stages. A distinction is also made between late and early (referring to time) and upper and lower (referring to layers of rock). It can all get terribly confusing to nonspecialists, but to a geologist these can be matters of passion. I have seen grown men glow incandescent with rage over this metaphorical millisecond in life's history, the British paleontologist Richard Fortey has written with regard to a long-running twentieth-century dispute over where the boundary lies between the Cambrian and Ordovician.

Reference

A Short History of Nearly Everything