What is the name of Odysseus's son?

Odysseus’s son is Telemachus.

Telemachus is the son of Odysseus and Penelope and the prince of Ithaca. When the Odyssey begins, Odysseus has been absent for twenty years, and Telemachus has grown up without his father while suitors consume the family’s wealth and pressure Penelope to remarry.

The first four books are traditionally called the Telemachy because they follow Telemachus’s attempt to learn what happened to Odysseus. Guided by Athena, he visits Nestor at Pylos and Menelaus and Helen at Sparta, gathering news about the long-delayed homecoming.

Telemachus later reunites with his disguised father at Eumaeus’s hut. Once Odysseus reveals himself, father and son plan the destruction of the suitors and fight together in Ithaca’s palace. Telemachus is sometimes confused with Telegonus, but Telegonus belongs to later traditions and is Odysseus’s son by Circe, not the son featured in Homer’s Odyssey.