Repeated and alternate treatment of a nickel surface with Na2PtCl6, CoCl2, and NaBH4 solutions with the general formula [n(Co(OH)2–mPt(0)]k (n and m denote the number of Successive Ionic layers Deposition (SILD) cycles in the preparation of Co(OH)2 and Pt(0), respectively, and k is the number of their repetitions] leads to the formation of multilayer nanocomposites consisting of Co(OH)2 nanosheets and Pt(0) nanoparticles. Their studying by TEM, SEM, XPS, and X-ray diffraction methods showed that it is possible to change morphological characteristics of both nanosheets and nanoparticles, and also of the arrays which they form, by changing the synthesis program, i.e., for example, the n and m values. The most significant differences in such characteristics are observed for samples obtained at n and m values preset in the range of 1–5. The study of the electrocatalytic behavior of such samples in the reaction of hydrogen evolution during the electrolysis of water in the alkaline region showed that the overvoltage values in the series of such samples are largely determined by the synthesis conditions, and their analyzing in the series of samples obtained according to various algorithms allows us to choose the conditions that provide the lowest overvoltage values.