We don't get to rename Perl. Perl is Larry's language. The various revisions of Larry's language over the years have addressed Larry's concerns and needs at the time. As those concerns go, so goes his language.
Right now, he's working on the sixth revision of that language, and it looks like it's going to be a big one, but it's still his language. The family resemblance is still there. Sure, he could go all Wirthy on us and call it, I dunno, Titania, but if he does, that's his decision, not ours.
Until Larry makes the unlikely decision to rename, the way we distinguish between Perl 5 and Perl 6 is pretty straightforward. We call Perl 5 "Perl 5" and we call Perl 6 "Perl 6". The meaning of 'Perl', unqualified, will shift over time, just as it shifted from carrying an implicit "4" to carrying an implicity "5" during the last great revision shift.