Lesniewski started to work on the theory in 1914 and in 1916 he published what he called this "theory of manifolds" or "theory of collective sets". No use of the word there.
It seems that the use of the term "Mereology" begins with his "On the foundations of mathematics" series starting in 1927, but I don't have his collected works handy now do double-check that. This is also confirmed by this footnote:
@ Rafal, thanks for this. Do you know when mereology was taken out of the more mathematical and calculus based philosophical work of authors such as Lesniewski? Are you aware of the term mereology being used in a more general philosophical or psychological sense to mean parts and wholes?
Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole.[1] Its roots can be traced back to the early days of philosophy, beginning with the Presocratics and continuing throughout the writings of Plato (especially the Parmenides and the Thaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium), and Boethius (especially De Divisione and In Ciceronis Topica). Mereology occupies a prominent role also in the writings of medieval ontologists and scholastic philosophers such as Garland the Computist, Peter Abelard, Thomas Aquinas, Raymond Lull, John Duns Scotus, Walter Burley, William of Ockham, and Jean Buridan, as well as in Jungius's Logica Hamburgensis (1638), Leibniz's Dissertatio de arte combinatoria (1666) and Monadology (1714), and Kant's early writings (the Gedanken of 1747 and the Monadologia physica of 1756). As a formal theory of parthood relations, however, mereology made its way into our times mainly through the work of Franz Brentano and of his pupils, especially Husserl's third Logical Investigation (1901). The latter may rightly be considered the first attempt at a thorough formulation of a theory, though in a format that makes it difficult to disentangle the analysis of mereological concepts from that of other ontologically relevant notions (such as the relation of ontological dependence).[2] It is not until Leśniewski's Foundations of a General Theory of Manifolds (1916) and his Foundations of Mathematics (1927–1931) that a pure theory of part-relations was given an exact formulation.[3] And because Leśniewski's work was largely inaccessible to non-speakers of Polish, it is only with the publication of Leonard and Goodman's The Calculus of Individuals (1940), partly under the influence of Whitehead, that mereology has become a chapter of central interest for modern ontologists and metaphysicians.[4]
Stanisław Leśniewski (1886–1939) was one of the principal founders and movers of the school of logic that flourished in Warsaw between the two world wars. He was the originator of an unorthodox system of the foundations of mathematics, based on three formal systems: Protothetic, a logic of propositions and their functions; Ontology: a logic of names, and functors of arbitrary order; and Mereology, a general theory of part and whole. His concern for utmost rigor in the formalization and execution of logic, coupled with a nominalistic rejection of abstract entities, led to a precise but highly unusual metalogic. His strictures on correctly distinguishing use from mention of expressions, his canons of correct definition, and his mereology, have all informed the logical mainstream, but the majority of his logical views and innovations have not been widely adopted. Despite this, his influence as a teacher and as a motor for logical innovation are widely acknowledged. He remains one of logic's most original figures.