The IUPAC name of $\left[\mathrm{Ni}(\mathrm{CO}{)}_4\right]$ is 

tetracarbonylnickel(0)

The NiCO₄ IUPAC name is tetracarbonylnickel(0).

Explanation: Nickel carbonyl (Ni(CO)₄) is an organometallic compound composed of a nickel atom surrounded by four carbonyl (CO) ligands. Each carbonyl ligand is a neutral molecule consisting of a carbon atom triple-bonded to an oxygen atom, which coordinates to the nickel through its carbon atom. This makes the compound a neutral, zero-valent complex of nickel, hence the "(0)" in its IUPAC name.

The prefix "tetra-" signifies the four carbonyl ligands attached to the central nickel atom, while "nickel" is the name of the metal. Organometallic compounds like Ni(CO)₄ are significant in chemistry due to their roles in catalysis and as intermediates in various industrial processes.

Ni(CO)₄, also known as nickel carbonyl, is a colorless liquid at room temperature and is highly toxic. Its structure and properties make it an important subject in coordination and organometallic chemistry.

Thus, the Ni CO₄ IUPAC name is tetracarbonylnickel(0), and the correct answer is option B.