Some people call the "long fist" system as northern Shaolin system. My old school had name "Northern Shaolin Institute". Today, I may use "Muslim Long Fist" instead.
Many Shaolin arts came from outside CMA system such as long fist. It's difficult to tell which is chicken and which is egg.
Using the Shaolin name has been going on for so long, it's practically it's own tradition. To make it even more confusing, there's debate about how much martial arts the Shaolin themselves did, before the name became popular.