The correct name for the ionic compound HgI2 is mercuric iodide.
Alternatively, it can also be referred to as mercury(II) iodide, but the term "mercuric iodide" is commonly used in nomenclature. The "II" indicates the oxidation state of mercury, which is +2 in this compound.
So, both "mercuric iodide" and "mercury(II) iodide" are acceptable names, but the best answer from your options is mercuric iodide.