Step 1: Understanding the Concept:
In coordination nomenclature, we name the cation first, then the ligands in alphabetical order, followed by the central metal of the complex anion with the suffix "-ate."
Step 2: Formula Application:
In $\mathrm{Hg[Co(SCN)_4]}$, Mercury is the cation ($Hg^{2+}$). The complex anion is $[Co(SCN)_4]^{2-}$.
Let $x$ be the oxidation state of Cobalt: $x + 4(-1) = -2 \implies x = +2$.
Step 3: Explanation:
The ligand $SCN$ is named "thiocyanato-S" because it is linked through the Sulfur atom. Since the complex is an anion, Cobalt becomes "cobaltate."
Step 4: Final Answer:
The IUPAC name is Mercury (II) tetrathiocyanato - S - cobaltate (II).