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?
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.
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 the start of your turn 2 pieces (or more) of yours are attacked. In this case, since one brought this situation upon themselves, it is called a self-fork.
If you move a piece into a position where it can be captured "for free", you are leaving the piece en prise. White's Rf4 in this game, therefore, leaves two pieces en prise.
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.
