Linnean taxonomy was very much the progression and refinement of earlier taxonomic thoughts. This answer draws heavily from "Linnaeus as an Intermediary between Ancient and Modern Zoölogy; His Views on the Class Mammalia" by W. K. Gregory (1908).
Gregory notes several major figures in the history of taxonomic nomenclature before Linnaeus:
Aristotle (384–322 BC): In On the Parts of Animals, Aristotle began to group and classify animals by certain characteristics, such as teeth, hooves, etc. Aristotle considered the state of nomenclature in The History of Animals (Book I, part 6), where he wrote:
In the genus that combines all viviparous quadrupeds are many species,
but under no common appellation. They are only named as it were one by
one, as we say man, lion, stag, horse, dog, and so on; though, by the
way, there is a sort of genus that embraces all creatures that have
bushy manes and bushy tails, such as the horse, the ass, the mule, the
jennet, and the animals that are called Hemioni in Syria,-from their
externally resembling mules, though they are not strictly of the same
species. And that they are not so is proved by the fact that they mate
with and breed from one another. For all these reasons, we must take
animals species by species, and discuss their peculiarities severally'
Andrea Cesalpino (1519-1603): A botanist, who in De Plantis (1583), divided plants into ten large classes based on morphology such as fruits and seeds, and then further subdivided them. He gave them monomial names.
- John Ray (1627-1705): An English naturalist, he made important steps in taxomony. For example, he classified many plants in his publication of Historia Plantarum. Gregory describes that:
Ray also used the term "species" in quite a Linnaean manner, as in the
names Ovis laticauda, Ovis strepsiceros and Ovis domestica. In form,
at least, this foreshadows the binomial system of nomenclature and the
recognition of the species in general as supposedly objective reality
and the unit of classification.The form of Ray's specific definitions
seems, however, to imply that the term "species" in Ray's mind was
often more a "differentia," or specific adjective modifying the
generic concept than a fully developed substantive name, and Ray did
not apparently realize the convenience of applying the binomial method
of nomenclature universally."
While there were many other figures involved in the development of modern taxonomy and taxonomial nomenclature, these individuals illustrate well that Linnaeus's binomial nomenclature, while an important step, was not an enormous leap. The idea of classifying species pre-dates Aristotle, and while monomial names for species were mostly used up until the seventeenth century, Linneaus was not the first to use binomial names for species, although he was the first to do so systematically across many classes of living things.