What is the name of the bard who is spared by Odysseus?

The bard spared by Odysseus is Phemius.

Phemius is the Ithacan singer who performs in the palace while Odysseus is away. The suitors of Penelope compel him to entertain them, including with songs about the Greek warriors’ return from Troy. His performance troubles Penelope because it reminds her of Odysseus’s long absence, but Telemachus defends the singer’s right to choose his subject.

When Odysseus returns in disguise and destroys the suitors, Phemius fears that he will be treated as one of their collaborators. He seizes a chance to plead for his life, explaining that he served the suitors unwillingly rather than out of loyalty. Telemachus confirms the truth of his defense, and Odysseus spares him.

Phemius is distinct from Demodocus, the blind bard who sings for the Phaeacians in another part of the Odyssey. The poem also includes Medon, a herald who survives the massacre, but Medon is not the bard. After the killings, Odysseus orders Phemius to perform wedding songs loudly, helping conceal what has happened until Odysseus and Telemachus can leave the palace.