I don't know if there is already name for this, but I like to call this type of puzzle an "onlymate": the only legal move delivers mate!

The challenge is not in the puzzle itself, but in the construction thereof. Can you create an onlymate?

Easy

Something a little different this time...

That last one is really nice.

But that's flawed!!! it's check but not check mate, the rook can take the bishop and there's a few pices able to block the bishop!!

No, it's a double check.

At first, I didn't understand your Frampits vs Totem puzzle as I thought, "It must be black's move and he can go ...Kh7 etc,  Edit: or ...RxBe3 mate or ...QxBe3.  Then I understood.

Clever.  Hard to believe it is from a game.

here's two possibly devious cases!