Right of publicity

Separate from copyright, which covers the recording, while this covers the person inside it. In the United States it varies state by state, some giving it statutory force and others treating it as a privacy claim, and other countries reach similar ground through image or personality rights.

For a creator it bites on the commercial side. Putting somebody on merchandise or inside a sponsored segment without permission is where claims come from, while news, comment and criticism get more room. A written release from anyone identifiable in something you intend to sell is the habit that keeps you out of it.