The most common arrangement of a Link Motion, with the expansion link moving up and down is indeed known as Stephenson, although it was invented by his employee Howe.
If the expansion link moves on a fixed rocker, and a radius rod to the valve rod moves up and down the link, then the link is curved the other way, towards the cylinder, and it is called Gooch.
If the expansion link and radius rod both move, in opposite directions, and the expansion link slot is straight, then it is called Allan.