Savoy is also name of a region of Europe traditionally in the north-western part of Italy, but largely absorbed into France (Savoie) in 1860 as part of a large-scale political deal that brought about the unification of Italy.
From 1416 to 1714 it was the main portion of the independent Duchy of Savoy.
It is worth noting that the seat of the Savoyards remained in Turin, in Piedmont, and the name change was really just a political maneuver designed to secure a promotion from Duke to King.
Sardinia was economically and politically moribund in comparison to Savoy and Piedmont, but traditionally had the title "King" associated with its possession (Regnum Sardiniae et Corsicae), hence the redubbing.