With PSO2 having more than one Dark Falz, it's clear enough that not every Dark Falz is the same character even if you can connect the stories. To that end I think they should have their own names (if they haven't been retconned in), even if only just for fun.
Classic: Dark Falz Proto/Zero-One (This one might not actually be the first so Zero-One instead of One)
PSO/0: Dark Falz Ringo (and yes, I know this means "apple", red just happens to always be the first color that comes to my mind when thinking of apples, even though my favorite kind is granny smith, which are green, also I couldn't think of a better ring-related pun, as a ring-related pun also ties into the shapes of "O" and "0" as part of the wordplay)
PSU/PSP/PSP2: Dark Falz Tane
Also for the heck of it, Idola: IDK if this one has a name and I don't know anything about the story but the look strikes me as a Dark Falz Pierrot