They certainly don't have anything like that in most of the US.
Sometimes there's a breakfast "steak" egg and cheese bagel, but that's clearly not what you're talking about, and it's as much of a "steak" as a McRib is ribs...
(Also what does a steak sliced in two even mean? Steaks can be cut whatever thickness you want, every steak is just a slice of a larger steak. And the total amount of meat is determined by pre-portioned weight anyways.)
The burger was advertised as having two beef patty but the combined height, and hence volume of the two patties lying on top of one another was that of a single beef patty that you could buy in supermarket.
And what do you call an actual steak to differentiate? I.e. a seared single portion of whole sliced beef, not ground? Or is it just clear from context?