Common names have little meaning. You can call it what you want.
There is no difference between calling them yabbies, crayfish, crawfish, lobsters or long crabs.
Some species of crayfish are illegal is some states, that is true, but those species are demarcated by Latin name, not by what you chose to call them that day. They are illegal as they are invasive to some areas and are outcompeting the native crays. Most of the introduced species are either pet releases or releases from educational facilities. It is really common for educational suppliers to stock odd ball crayfish that end up in second grade classrooms and then released to a creek in June when school is out.