April 2009 video clip on the symbol S by SixtySymbols.

In thermodynamics symbols, S is the symbol for entropy, assigned by German physicist Rudolf Clausius. Specifically on April 24, 1865, Clausius assigned the symbol as follows: [1]

“I propose to call S the entropy of the body, from the Greek word τροπή, transformation.”

Symbol etymology
It is argued that use of the letter S to represent the thermodynamic quantity of entropy is used on the model of French physicist Sadi Carnot who used small "s" for heat; or possibly it could have been named, in an unwritten manner, in honor of (S. Carnot), whose 1824 treatise On the Motive Power of Fire is what gave birth to the formulation of entropy over a period of fifteen years (1850-1865) by Clausius. To argue in favor of the latter hypothesis, one will note the salient use of the abbreviation “S.” on the first page of Clausius’ famous first memoir “On the Moving Force of Heat”, where he states: [2]

“The most important research done [on the mechanical theory of heat] is that of S. Carnot.”

In the foot notes to this comment, Clausius goes on to explain how he not yet obtained a copy of Carnot’s work but that he knows it “solely through the writings of Clapeyron and Thomson.” He then spends the next fifteen years thinking and theorizing about this paper; thus coming to call his famous variable entropy by the symbol S at the end of this prolonged effort.

An arguable point is that if Clausius consciously used S in honor of Sadi Carnot, why didn’t he use the symbol C, similar to how G is named after Willard Gibbs. One reason might be that C was already in use as heat capacity, as adopted by Joseph Black in the late 18th century.

Other
In 1872, Austrian physicist Ludwig Boltzmann used the symbol E to represent Clausius' entropy. [3] In 1873, American engineer Willard Gibbs used the Greek symbol eta η to represent Clausius' entropy. [4]

See also
● S = k ln W

References
1. (a) Clausius, R. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies (terms: “entropy” and “S”, pgs. 357, 363, 367) (URL). London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
(b) Read at the Philosophical Society of Zurich on the 24th of April, 1865, published in the Vierteljahrsschrift of this society, Bd. x. S. 1.; Pogg. Ann. July, 1865, Bd. cxxv. S. 353; Journ. de Liouville, 2e ser. t. x. p. 361.
2. Clausius, Rudolf. (1850). "On the Motive Power of Heat, and on the Laws which may be deduced from it for the Theory of Heat", (term: “S. Carnot”, pg. 1) Communicated in the Academy of Berlin, Feb.; Published in Poggendorff's Annalen der Physick, March-April. LXXIX, 368, 500.
3. Boltzmann, Ludwig. (1872). "Further Studies on the Thermal Equilibrium of Gas Molecules" (“Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen”), in Sitzungsberichte der Akademie der Wissenschaften, Mathematische-Naturwissenschaftliche Klasse (pgs. 275-370; term: "entropy" symbol "E", pgs. 263, 308, 346, etc), Bd. 66, Dritte Heft, Zweite Abteilung, Vienna: Gerold.
4. Gibbs, J. Willard. (1873). "Graphical Methods in the Thermodynamics of Fluids" (symbol table, pg. 1), Transactions of the Connecticut Academy, I. pp. 309-342, April-May.