The Persian commander who stayed in Greece after Xerxes withdrew to Asia was Mardonius.
Mardonius was a Persian general and a close relative of Xerxes I. After the Persian defeat at Salamis in 480 BC, he persuaded Xerxes to return to Asia with much of the army while he remained behind to continue the campaign.
Mardonius wintered in Greece and later commanded the Persian forces at Plataea in 479 BC. He briefly recaptured Athens before the allied Greek victory at Plataea ended the Persian invasion. Mardonius was killed during that battle.
The other options are associated with Persian history but not this role: Artabanus advised Xerxes cautiously, while Megabazus and Hydarnes were different Persian commanders. Mardonius is the canonical answer.