In all honestly, it doesn't matter. The official name of the polity was Kingdom of Sardinia, but the government, ruling class, and center of population was in Piedmont; hence the most used demonym when referring to people and things originating from it is "Piedmontese." To avoid any confusion by those unfamiliar with the minutiae of the order of precedence in the Kingdom's titles, it is often referred to as either "Sardinia-Piedmont" or "Piedmont-Sardinia." Neither title is official, so neither is incorrect.

If we really want to get into the pedantry of that state founded in 1718 due to curious circumstances following the War of Spanish Succession, it was in reality composed of three personal unions (which later became four after the annexation of the Republic of Genoa in 1814). The three states were the Kingdom of Sardinia; the County of Nice; and the Duchy of Savoy, which included the sub-divisions of the Principality of Piedmont, the Marquisate of Saluzzo, the Duchy of Monferrant, and the Marquisate of Susa. Because the ruler's highest ranking title was that of King of Sardinia, that's the most commonly used name for the entire polity, however the form "States belonging to the King of Sardinia" does appear in some legal texts ("Stati del Re di Sardegna"). If you want to get really esoteric, you can also call it the "Sabaud Kingdom" using an archaic demonym for Savoy and its ruling house (or maybe the demonym's "Sabaudian?" I'm not sure, the Italian is Sabaudo)

With the "Perfect Fusion" ("Fusione Perfetta") of 1847, a single unitary state was founded, centralizing all governmental institutions in Turin. Because the monarch's titles were, in order of rank: King of Sardinia, Prince of Piedmont, Duke of Genoa, and Duke of Savoy, the state continued to be called "Kingdom of Sardinia."

I didn't remember which form I favored, so I just ran a word-count and I discovered I favor the form, "Kingdom of Sardinia-Piedmont," although there's one paper I wrote where I inexplicably switch to "Kingdom of Piedmont-Sardinia" in my conclusion.