Answer
The full name is lead(II) iodide .
Work Step by Step
The charge on Pb must be 2+ for the compound to be charge-neutral with two $I^{-}$ anions. The name for $PbI_{2}$ is the name of the cation, lead, followed by the charge of the cation in parentheses (II) and the base name of the anion, iod, with the ending - ide. The full name is lead(II) iodide.