What was the name of Orpheus's wife?

According to a fragment of Pindar, and Apollodorus Orpheus' father was Oeagrus (Οίαγρος) a Thracian king (or, according to another version of the story, the god Apollo); his mother was the muse Calliope or a daughter of Pierus son of Makednos.

As you can gather from the above, the trouble with the Greek myths is that there are always alternative stories.