The double agent (often abbreviated DA) is a cast member at the party. The spy can select which character will be the double agent during game setup. The Contact Double Agent mission requires the spy to send a message to the double agent; see that article for more information.
The spy can identify the double agent by the yellow triangle over their head. What the sniper knows about the double agent depends on the map: some maps reveal the double agent to the sniper, others don't, and still others show the sniper several "suspected double agents." Any suspected double agents that are revealed to the sniper are marked with a yellow triangle; one of them will be the actual double agent, and none of them will be the spy. (Note that any map which displays suspected double agents to the sniper will do so even when the Contact Double Agent mission is unavailable.) Other than the actual double agent, the spy does not know which characters are marked as suspected double agents for the sniper; if any are shown, the game selects them at random.
A double agent or suspected double agent will never join a conversation circle which already contains a double agent or suspected double agent.