Who is the son of Nestor who accompanies Telemachus?

The son of Nestor who accompanies Telemachus is Peisistratus. When Telemachus travels from Ithaca to Pylos and then Sparta to seek news of Odysseus, Nestor welcomes him and assigns his youngest son to accompany him.

Peisistratus first appears as a hospitable companion during the journey. He helps Telemachus travel safely, shares meals with him, and takes part in the visit to Menelaus and Helen in Sparta. His presence gives Telemachus a trusted peer while the young prince begins acting independently of his absent father.

The character belongs to Nestor’s large family. Ancient sources differ over Nestor’s wife—Homer names Eurydice, while later genealogical traditions give Anaxibia—but they identify Peisistratus as Nestor’s son. He is also associated with Antilochus and Thrasymedes, Nestor’s better-known sons from the Trojan War generation.

Antilochus and Thrasymedes are therefore tempting wrong answers because they are Nestor’s sons, but neither is Telemachus’ traveling companion. Perseus is another brother in some genealogical lists, not the companion in the Odyssey.