The name of the hero who sailed with Odysseus in Greek mythology is Ajax or Achilles, depending on the context. Ajax was a formidable warrior known for his size and strength, participating in the Trojan War and featuring prominently in Homer’s "Iliad." Conversely, Achilles, famed for his near invincibility, played a crucial role in Odysseus's adventures. Both heroes exemplify different aspects of heroism and valor in mythology, showcasing the complexities of mortality and the pursuit of glory in the ancient world.