In the position below (Short vs Ponomariov 2003), White has just played Re4-f4, which is allowing the g5 pawn to attack both the rook and the bishop.
In general, what do we call a move that allows the opponent to attack two pieces without making another move?
It is called a fork or a double attack in a normal case. A normal case is when before the opponent's turn neither piece is attacked and then by your turn both pieces (or more) are attacked. In this case, since one brought this situation upon themselves (and forks are generally undesirable), it is called a self-fork.
what do we call a move that allows the opponent to attack two pieces without making another move?
When the opponent makes a move which attacks two pieces at the same time with the same piece it's called a fork, so what you describe is called a self-fork.
Re4-f4 was played, but both the rook and bishop were hanging before the move. So I wouldn't call it a self-fork - there is not even one extra piece attacked, let alone the two you are getting in a regular fork.
I don't know what I would call it though. Misdirection? Overload? Tempo something? Tal attack? :D It is probably rare enough it doesn't have a name.
Note that there are possible self-fork moves - where a single move adds 2 extra pieces to be attacked. For example: a white pawn was on e4 and moves to e5, with pieces on f4, f3 and d3. Black has a rook on a4, bishop on c6 and queen on g6.
