Source: Woodcraft Folk Games Games Games
More an icebreaker/introduction than a full-on folk game, but possibly a good way to learn everyone's name.
Play some music. When the music starts, all the players move round the room in any direction. When the music stops, each player links arms with the person closest to them, shakes their hand and introduces themselves. When the music starts again, players stay linked and continue around the room. When the music stops, each pair links one arm with another pair, and everyone introduces themselves.
Play continues until everyone is linked in one long chain.