What is the name of the seer who accompanies Telemachus back to Ithaca?

The seer who accompanies Telemachus back to Ithaca is Theoclymenus.

Theoclymenus is a prophet from Argos who meets Telemachus at Pylos during the young prince’s search for news of Odysseus. He has fled Argos after killing a relative and seeks refuge aboard Telemachus’s ship. Telemachus accepts him as a guest, and the two travel together to Ithaca in Book 15 of Homer’s Odyssey.

Once in Ithaca, Theoclymenus interprets bird omens and predicts that Telemachus will become the head of Ithaca’s royal household. He also claims that Odysseus is already on the island, secretly observing events in disguise. Penelope does not believe this prophecy, and the suitors mock Theoclymenus when he foresees their impending deaths.

A common mix-up is Mentor, who advises Telemachus and is sometimes associated with his journey. Mentes is another identity used by Athena in disguise, while Halitherses is an older Ithacan prophet. Theoclymenus is the specific seer who travels with Telemachus from Pylos to Ithaca.