Everyone takes a seat, there are 3 or 4 seats on a couch which is
the goal, and one empty seat.

Each team is trying to fill the couch with their players.

Everyone's name is written on a piece of paper and each player
gets a random name that is not their actual name, this name
is a secret.

Whomever is to the left of the empty seat calls a name that is
not the one on their piece of paper (and wasn't the last name called).

The person holding that name needs to take the empty seat.

Play continues to the person on the left of the new empty seat.

Alternative:  Have 'n' teams with 3-4 players in each time (size of the couch).
Alternative:  Everytime someone's name is called, they trade papers with the caller.