Answer
The full name is lead(IV) iodide.
Work Step by Step
The charge on Pb must be 4+ for the compound to be charge-neutral with four I- anions. The name for $PbI_{4}$ is the name of the cation, lead, followed by the charge of the cation in parentheses (IV) and the base name of the anion, iod, with the ending - ide. The full name is lead(IV) iodide.